# FIN700 Financial Management Proof Reading Service ## Question 1

### a) Three-period certainty model problem

John Brown earns sole income from the trust and the capital market rate of interest is 5% per annum. John will receive \$40,000 now in Year 0, \$30,000 at the end of Year 1 and \$60,000 at the end of Year 2. In this way John will have the following amounts as funds during the period of three years:

Year 0 = \$40,000

Year 1 = \$40,000 + \$40,000*0.05 + \$30,000

= \$42,000 + \$30,000

= \$72,000

Year 2 = \$42,000+ \$42,000*0.05 + \$30,000 + \$30,000*0.05 + \$60,000

= \$44,100 + \$31,500 + \$60,000

= \$135,600 Thus, John Brown will have an amount of \$135,600 in two years’ time of he does not consume during this period (Fair, 2014). If John consumes as per his \$32,000 now and \$ 42,000 in one year then the amount for consumption remaining with him at the end of each period will be as follows:

Year 0 = \$40,000 – \$32,000

= \$8,000

Year 1 = \$8,000 + \$8,000*0.05 + \$30,000

= \$8,400 +\$30,000

= \$38,400

Here, John wishes to consume \$42,000 but he has funds of \$38,400 only and therefore he cannot consume \$42,000. He will have to limit his consumption up to \$38,400.

### b) Capital Asset Pricing Model (CAPM)

 Name of company Expected return Beta Formula CAPM Shamrock Ltd. 10.40% 0.4 =8% + 0.4*6% 10.40% Camellia Ltd. 12.90% 0.7 =8% + 0.7*6% 12.20% Rose Ltd. 13.80% 1.1 =8% + 1.1*6% 14.600% Daffodil Ltd. 17.60% 1.6 =8% + 1.6*6% 17.600%

#### (i) Undervaluation and overvaluation of shares

Shamrock Ltd. = In this case, expected return is 10.40% and expected return using the CAPM model is 10.40%. Both the expected return and expected return using CAPM is same. This shows that shares are correctly valued.

Camellia Ltd. = In this case, expected return is 12.90% and expected return using the CAPM model is 12.20%. Expected return using CAPM is lower than the expected return. This shows that shares are overvalued.

Rose Ltd. = In this case expected return is 13.80% and expected return using the CAPM model is 14.60%. Expected return using CAPM is higher than the expected return. This shows that shares are undervalued (Noda, et. al., 2016).

Daffodil Ltd. =   In this case, expected return is 17.60% and expected return using the CAPM model is 17.60%. Both the expected return and expected return using CAPM is same. This shows that shares are correctly valued.

#### (ii) Security market line graph (SML)

This graph shows the presentation of CAPM formula. This chart represents beta on the X axis and returns on the Y axis. This chart shows expected return on securities on beta.

 Name of company CAPM Beta Risk-free rate 8% 0 Shamrock Ltd 10.40% 0.4 Camellia Ltd 12.20% 0.7 Rose Ltd 14.60% 1.1 Daffodil Ltd 17.60% 1.6 This security market line graph shows expected return on beta. As described in the table X-axis of this chart shows beta and Y axis of this chart shows expected return on securities (Elbannan, 2014).

### Question 2

#### a) Time value of money and deferred perpetuities

(i) Present value of the constant income flows at the beginning of the eighth year

 Year Return PV factor Present value 1 0 0.943396 0 2 0 0.889996 0 3 0 0.839619 0 4 0 0.792094 0 5 \$80,000 0.747258 \$59,780.65 6 \$130,000 0.704961 \$91,644.87 7 \$180,000 0.665057 \$119,710.28 Inflow at beginning of eight year \$271,135.80

This calculation shows that the present value of income cash flow at the beginning of the eighth year will be \$271,135.80.

(ii) Present value of whole income stream

Perpetuity:Perpetuity is a type of annuity when an infinite amount is received for periodic payments. Perpetuity formula is applied for calculation of present value of such annuity amount. This helps in calculation of present value of future cash flows (Yu, et. al., 2010). The formula for calculation of present value of a perpetuity is as follows.

Present value of perpetuity= D/R

Present value of perpetuity= \$250000+ (\$271,135.80/6%)

Present value of perpetuity= \$4,437,802.47

This shows that present value of whole stream income is \$4,437,802.47.

#### b) Loan repayments and loan terms

Lisa Brown obtained a loan of \$700,000 with equal monthly repayments over 12 years and the rate of interest is 8.4% compounded monthly. The installment amounts for monthly repayment can be calculated as follows in excel:

Instalment = PMT (rate, nper, PV)

= \$7,731.54

The Balance of the loan at the end of the second year can be calculated as follows:

 Month Principal Interest Balance 1 2832 4900 697168 2 2852 4880 694316 3 2872 4860 691444 4 2892 4840 688552 5 2912 4820 685640 6 2933 4799 682708 7 2953 4779 679755 8 2974 4758 676781 9 2995 4737 673787 10 3015 4717 670771 11 3037 4695 667734 12 3058 4674 664677 13 3079 4653 661597 14 3101 4631 658497 15 3123 4609 655374 16 3144 4588 652230 17 3166 4566 649063 18 3189 4543 645875 19 3211 4521 642664 20 3233 4499 639430 21 3256 4476 636174 22 3279 4453 632896 23 3302 4430 629594 24 3325 4407 626269

Thus, the Balance of loan at the end of the second year is \$626,269

Now, Lisa Brown has two options. The first alternative is to increase the monthly repayment and the second alternative is to extend the period of the loan.

First Option

If Lisa accepts the first alternative then in such case the revised installments calculated using excel will be as follows:

Revised Instalments = PMT (10.2%/12, 12*10, 626,269)

= \$8,346

Thus, the new monthly repayment will be \$8,346 if Lisa accepts the first alternative.

Second alternative

If Lisa accepts the second alternatives then the installment amount will be \$7,732. In this case, the number of installments or the period of loan will increase. The calculated number of periods using interpolation for an instalment of \$7,731 compounded monthly at the rate of 10.2% per annum to repay \$626,269 will be 138 months or 11.5 years (Ally, 2015). Thus the extra period will be 11.5 years – 10 years = 1.5 years. Therefore if Lisa adopts the second alternative, the extra period that will be added to her loan period will be 1.5 years or 18 months.

### Question 3

#### a) Risk and Return

Expected Return = WA* ER(A) + WB* ER(B)

Where W is the weight of security

And ER is the Expected Return of security\

Billy’s portfolio consists of two shares A and B. He has invested 1/4th of his investment in Share A and remaining 3/4th in Share B. Thus, W(A) = 0.25 and W(B) = 0.75.The expected return from Share A is 14% and that of Share B is 20%. Thus, ER(A) = 14% and ER(B) = 20%.

Expected Return on Billy’s Portfolio = W(A)* ER(A) + WB* ER(B)

= 0.25*14% + 0.75*20%

= 18.5%

Thus the expected return of Billy’s portfolio is 18.5%

Standard Deviation of Portfolio can be calculated using the following formula:

Portfolio Standard Deviation = √WA2σA+ WB2σB2+ 2WA WBσAσBp

Where W is the weight of security,

σ is the standard deviation of security

And p is the correlation of the security

The Standard deviation of Share A in Billy’s portfolio is 17% and that of Share B is 24% and the correlation between the returns of the two shares is 0.5 (Gajera, et. al., 2015).

Standard Deviation of Billy’s portfolio

=√0.25*0.25*0.17*0.17 + 0.75*0.75*0.24*0.24 + 2*0.25*0.75*0.17*0.24*0.5

=√0.041856

= 0.2045

= 20.45%

Billy has currently invested in a two share portfolio. He can either retain his investments in both the shares in the ratio of 1:3 as presently held or he can make 100% investment in any on the two shares. In order to make the recommendation about whether he shall maintain its existing two-share portfolio or he shall invest all his funds in one of the two securities the analysis can be made as follows:

 Portfolio Expected Return Standard Deviation One-quarter investment in Share A and three-quarter investment in Share B 18.5% 20.45% 100% investment in Share A 14% 17% 100% investment in Share B 20% 24%

It can be observed from the above table that both the expected return and standard deviation of Share A is higher and similarly for Share B both the return and risk is low. Win case of two share portfolios both the risk and return are medium. Thus, Billy is recommended to maintain its two share portfolio since in this case, he will be able to earn a good return with a medium level of risk (Merriman and Nam, 2015). However, if Billy wishes to invest in one of the two shares completely then he shall invest his funds in Share A since it has a lower risk as compared to that of Share B and has the potential to earn higher returns with lesser risk. If we compare the returns and risk of each of the two shares from the present risk and return with the two shares portfolio, then it can be observed that Share A will give good returns with lesser risks and Share B will give higher returns with higher risks.

#### (b) Valuation of Bonds

(i)  Calculation of Price

Face value of bonds = \$100,000

Rate of interest up to 15th October 2016 = 8% per annum compounded half-yearly

Revised interest rate after 15th October 2016 = 8% + 2% = 10%

Future Value of Bond on 15th January 2017

= \$100,000 + \$100,000*0.08*92/365

= \$102,016.44

Future Value of Bond on 15th April 2017

= \$100,000 + \$100,000*0.08*182/365

= \$103,989.04

Calculation of price of bonds maturing on 15 April 2019

Present Value of Bond on 15th April 2017 = 103,989/PV Factor @ 4%, 4 half years

= \$103,989/0.855

= \$121,625

Sales value of Bond on 15 January 2017 = \$121,265/PV factor @2%, 4 quarters

= \$121,265/0.924

= \$131,239

Calculation of price of bonds maturing on 15 April 2023

Present Value of Bond on 15th April 2017 = 103,989/PV Factor @ 4%, 12 half years

= \$103,989/0.625

= \$166,382

Sales value of Bond on 15 January 2017 = \$166,382/PV factor @2%, 4 quarters

= \$166,382/0.924

= \$180,067

Thus the sales value of bond maturing in the year 2019 will be \$131,239 and the bonds maturing in the year 2023 will be \$180,067.

ii. Relative price movements in bonds

As evidenced in the above answer the price movements of both the bonds have been fluctuating. With the increase in the period of maturity, the value of bond also increases due to higher amounts of interest accumulated.

### Question 4

#### a) Capital Budgeting

 Year 0 1 2 3 4 5 Total Cost Equipment cost 400000 Interest payments 40000 40000 40000 40000 40000 Working capital 27,000 Lease compensation 22000 Overhauling expenses 10,000 10,000 Total costs 449,000 40,000 40,000 50,000 40,000 50,000 Present Value Factor @14% 1 0.877193 0.769468 0.674972 0.59208 0.03779 Present value of costs 449000 35087.72 30778.7 33748.58 23683.21 1889.508 574187.7 Benefits Reduction in labour cost after tax 119,000 119,000 119,000 119,000 119,000 Salvage value after tax 21,000 Recovery of working capital 18,900 Tax saving on depreciation 24000 24000 24000 24000 24000 Tax saving on interest expense 12000 12000 12000 12000 12000 Tax saving on overhauling expenses 3000 3000 Total Benefits 155,000 155,000 158,000 155,000 197,900 Present Value Factor @14% 1 0.877193 0.769468 0.674972 0.59208 0.03779 Present Value of benefits 0 135964.9 119267.5 106645.5 91772.44 7478.672 461129 Incremental cash flows -449000 100877.2 88488.77 72896.92 68089.23 5589.164

Above table shows the calculation of NPV and incremental cash flows.

(a) NPV =   Total cost-Total benefits

NPV = 574787.7- 461129

NPV = (113059)

In the present value terms, there is a net loss as total costs are higher than total benefits. Costs are higher than the benefits hence equipment will cause a net loss.

Calculation of incremental cash flow is shown in the above table.

(b) Purchase of equipment is to be finalized on the basis of NPV and this can be seen that the NPV of this project is negative which shows that this equipment will not be profitable for Capital Constructions Ltd (Becker and Ivashina, 2015). A cost of this equipment is higher than the benefits that are going to arise from this project. From this, it can be concluded that company should not purchase this equipment.

### References

Ally, A.M., 2015, “An Empirical Analysis of Financial Performance of Higher Education Students’ Loan Scheme (HESLS) in Tanzania”, International Journal of Management Sciences and Business Research, vol 4, issue 3, pp 45-59.\

Becker, B. and Ivashina, V., 2015. Reaching for yield in the bond market. The Journal of Finance, 70(5), pp.1863-1902.

Elbannan, M.A., 2014, “The capital asset pricing model: an overview of the theory”, International Journal of Economics and Finance, vol 7, issue 1, p.216.

Fair, R.C., 2014, “How might a central bank report uncertainty?”.

Gajera, M.A., Vyas, M.P. and Patoliya, M.P., 2015. Risk and Return Analysis Of BSE Small, Medium & Large Capitalization Indices. Scholedge International Journal of Management & Development ISSN 2394-3378, 2(4), pp.32-37.

Merriman, K.K. and Nam, D.I., 2015, “A Managerial Perspective on Risk and Return for Corporate Innovation Projects”, Organization Management Journal, vol 12, issue 4, pp.200-207.

Noda, R.F., Martelanc, R. and Kayo, E.K., 2016, “The earnings/price risk factor in capital asset pricing models”, Revista Contabilidade & Finanças, vol 27, issue 70, pp.67-79.

Yu, J.C., Wee, H.M., Widyadana, G.A. and Chang, J.Y., 2010, “The effects of inflation and time value of money on a production model with a random product life cycle”, Asia-Pacific Journal of Operational Research, vol 27, issue 04, pp.437-456.