Question

Problem 1

Consider the following two potential investments Nexit and Rexit. You plan to invest 8,000 KD in investment Nexit and 12,000 KD in investment Rexit.

Date	Return Nexit	Return Rexit
2016	0.03	-0.04
2017	-0.05	0.08
2018	0.08	0.07
2019	0.12	0.13

1. Build a portfolio consisting of Nexit and Rexit based on the information above.
2. Calculate the average return of the portfolio.
3. Calculate the risk of the portfolio.

Problem 2

SAGE Enterprises just paid a dividend of $2 per share. The current market price is $50 per share. Dividends are expected to grow at a constant rate “g”. The risk-free rate is equal to 3% and the share risk premium is equal to 5%.

1. Calculate the growth rate of dividends “g”.
2. Estimate the price of the share 5 years from today.

Problem 3

CAPITAL Partners has a beta of 1.1. The 3-month Treasury bill rate is 3%. The market risk premium is equal to 6%. The company wishes to fund a project through shares and bonds. 35% of funding came from bonds and the rest from shares. The marginal tax rate is equal to 15%. The yield to maturity on the bonds is equal to 7%.

1. Calculate the required rate of return on shares.
2. Calculate the Weighted Average Cost of Capital (WACC) of the firm.

Problem 4

Consider the following two projects and their respective cash flows. The WACC is equal to 10%.

Time	0	1	2	3	4
Project A	-10,000	3,000	5,000	4,000	-3,000
Project B	-11,000	5,000	4,000	-3,000	3,000

1. Calculate the NPV of each project.
2. Which project would you choose if A and B are mutually exclusive?

Problem 5

Consider a company that just paid a dividend a $3 per share. The dividends are expected to grow at the rate of 8% per year for the next 3 years and then at 4% thereafter.

1. Draw the timeline for the first 6 years.
2. Calculate the expected dividends for the next five years.

Answer 1

Problem 1:

(a) Building a portfolio consisting of Nexit and Rexit:

Particulars	Amount
Investment in Nexit	8,000KD
Investment in Rexit	12,000KD
Total amount invested in a portfolio consisting of Nexit and Rexit	20,000KD

(b) Calculation of average return of the Portfolio:

Average return of Nexit:

= (0.03-0.05+0.08+0.12)÷4

= 0.045

Average return of Rexit :

= (-0.04+0.08+0.07+0.13)÷4

= 0.06

Average return of the Portfolio

= 0.045×8,000÷20,000 + 0.06×12,000÷20,000

= 0.054

(c) Calculation of risk of the Portfolio:

Year	Returns of Nexit	Returns of Rexit	Deviation of return from mean of Nexit stock	Square of deviation of Nexit stock	Deviation of return from mean of Rexit stock	Square of deviation of Rexit stock
1	0.03	-0.04	-0.015	0.000225	-0.1	0.01
2	-0.05	0.08	-0.095	0.009025	0.02	0.0004
3	0.08	0.07	0.035	0.001225	0.01	0.0001
4	0.12	0.13	0.075	0.005625	0.07	0.0049
Average or Mean of the returns	0.045	0.06
Total				0.0161		0.0154

Standard deviation of Nexit: =√0.0161÷4 = 0.063

Standard deviation of Rexit: =√0.0154÷4 = 0.062

Standard deviation of portfolio: = 0.063×8,000÷20,000 + 0.062×12,000÷20,000

= 6.24%

Risk of the Portfolio = 6.24%

Problem 2: More information is required to solve this problem. i.e., β is required to solve this.

Problem 3:

(a) Calculation of required rate of return on shares:

​​​​​​Given,

Rf = 3%, β of equity = 1.1, Rm-Rf = 6%, weight of debt = 0.35, weight of equity = 0.65

Required rate of return (Ke) = Rf+β(Rm-Rf)

Ke = 0.03+1.1(0.06) = 9.6%

(b) Calculation of WACC of the firm:

Given, Yield of the bond = 7%, Tax rate= 15%

Cost of debt (Kd) = 7(1-0.15) = 5.95%

Weighted average cost of capital (WACC) = 5.95×0.35 + 9.6×0.65 = 8.32%

Problem 4:

(a) Calculation of NPV of each Project:

Project A:

Year	Cash flows	PVF@10%	Present value of cash flows
0	(10,000)	1	(10,000)
1	3,000	0.909	2,727
2	5,000	0.826	4,130
3	4,000	0.751	3,004
4	(3,000)	0.683	(2,049)
NPV	(2,188)

Project B:

Year	Cash flows	PVF@10%	Present value of cash flows
0	(11,000)	1	(11,000)
1	5,000	0.909	4,545
2	4,000	0.826	3,304
3	(3,000)	0.751	(2,253)
4	3,000	0.683	2,049
NPV	(3,355)

(b) Which project to choose if project A and B are mutually exclusive:

NPV of Project A = (2,218)

NPV of Project B = (3,355)

Conclusion: From the Calculations above both the projects are not profitable as NPV of both the projects are negative, but comparatively it is better to choose project A as NPV is better compared to Project A and as they are independent, project A is preferable.

Problem 5:

(a) Draw the timeline for first 6 years:

Given, Dividend per share just paid = $3 per share, Dividend Expected to grow @8% for next 3 years and 4% thereafter i.e.,

DPS1 = 3(1+0.08) = $3.24; DPS2 = 3.24(1+0.08) = $3.50; DPS3 = 3.50(1+0.08) = $3.78; DPS4 = 3.78(1+0.04) = $3.93; DPS5 = 3.93(1+0.04) = 4.09; DPS6 = 4.09(1+0.04) = $4.25

​​​​​​Please find the graph image that had been uploaded for timeline for first 6 years

(b) Calculation of expected dividends for next 5 years:

As Calculated above Expected dividends for next 5 years are as follows

DPS1 = $3.24

DPS2 = $3.50

DPS3 = $3.78

DPS 4 = $3.93

DPS5 = $4.09