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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.
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% 
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.
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 
Riskfree 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 Xaxis of this chart shows beta and Y axis of this chart shows expected return on securities (Elbannan, 2014).
(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.
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.
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 1/4^{th} of his investment in Share A and remaining 3/4^{th} 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 = √W_{A}^{2}σ_{A}^{2 }+ W_{B}^{2}σ_{B}^{2}+ 2W_{A} W_{B}σ_{A}σ_{B}p
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 twoshare 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 
Onequarter investment in Share A and threequarter 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.
(i) Calculation of Price
Face value of bonds = $100,000
Rate of interest up to 15^{th} October 2016 = 8% per annum compounded halfyearly
Revised interest rate after 15^{th} October 2016 = 8% + 2% = 10%
Future Value of Bond on 15^{th} January 2017
= $100,000 + $100,000*0.08*92/365
= $102,016.44
Future Value of Bond on 15^{th} 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 15^{th} 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 15^{th} 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.
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 costTotal 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.
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 4559.\
Becker, B. and Ivashina, V., 2015. Reaching for yield in the bond market. The Journal of Finance, 70(5), pp.18631902.
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 23943378, 2(4), pp.3237.
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.200207.
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.6779.
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”, AsiaPacific Journal of Operational Research, vol 27, issue 04, pp.437456.