Corporate Finance Assignment Presenting Financial Analysis of Business Cases

Question

Task: Prepare a corporate finance assignment addressing the following tasks:
MCQ Question 1:

Question C: Consider a portfolio of two risky assets with the following distribution of rates of return on risky assets. The portfolio is 55% Risky Asset 1 and 45% Risky Asset 2, and the correlation coefficient is 0.4.

Risky Asset 1 Risky Asset 2
Mean
Standard Deviation
0.16
0.25 0.09
0.18
What is the mean and standard deviation of this portfolio?
a. Mean: 0.1215 and Standard deviation: 0.15958
b. Mean: 0.1285 and Standard deviation: 0.18541
c. Mean: 0.1285 and Standard deviation: 0.25467
d. Mean: 0.2185 and Standard deviation: 0.25467

Question 2
A company is trying to decide between two mutually exclusive projects. Both require an initial investment of $100 million. Project A will generate an annual cash-flow of $18 million in perpetuity starting in exactly one-year time. Project B will generate a cash-flow of $12 million in exactly one year time, and growing at an annual rate of 4% per year in subsequent years. The cost of capital for both projects is 10% percent.

(a) Which project should the company choose?
(b) What is the IRR of each of these projects?

Question 3
Five banks offer deposit accounts at the following stated annual percentage rates:

Bank A: 10% APR compounded annually
Bank B: 9.8% APR compounded semi-annually
Bank C: 9.6% APR compounded quarterly
Bank D: 9.5% APR compounded monthly
Bank E: 9.4% APR compounded daily
Claire has inherited $150,000 and decides to invest the money in a 20 year deposit with a bank. She decides to invest the money with Bank E. If Claire had invested her money in the bank offering the best rate instead of Bank E, how much more money would she have had after 20 years?

Question 4
These are the projected levels of several key financial measures for a company you are valuing (in £ millions)
Year 1 Year 2 Year 3
Earnings before 150 180 200
Interest and taxes

Capital expenditure 50 75 85
Depreciation 25 30 30
The corporate tax rate is 40%. Net working capital remains constant. After Year 3 the free cash flow will grow at a constant rate of 5% per year. Calculate the free cash flows for this company for Years 1 through 3. What is the value of this corporation if the cost of capital is 10%? .

Question 5
a. What is the current price of a bond that has a coupon rate of 7%, a return rate of 8%, and a face value of $1,000? Assume that this bond will mature in five years. Compare the current price of the bond against its face value.

b. Calculate the coupon rate, and the yield to maturity for a bond that has $1,000 par value, pays $95 interest annually, matures in 25 years, and has a current price of $1,087.75.

Question 6
An investor has a $150,000 investment to allocate between a risky asset and a riskless asset. The expected rate of return for the risky asset is 0.18 and the expected rate of return for the riskless asset is 0.07. The standard deviation of the risky asset is 0.2. The investor requires a portfolio composition corresponding to an expected rate of return of 0.15.

(a) What proportion of the portfolio should be invested in the risky asset?
(b) What amount should be invested in the risky asset?
(c) What is the standard deviation of the portfolio?

Question 7
The capital structure of Quokku Corporation consists of $200 million of debt and $320 million of equity. Quokku Corporation has a marginal tax rate of 25%, beta of equity is 1.3, and beta of debt is 0.2. Assume also that the risk-free rate is 2% and the market risk premium is 5%.

(a) What is the expected return on Quokku’s debt? What is the expected return on Quokku’s equity?
(b) What is the after-tax WACC at the current leverage ratio?

Answer

MCQ Answer 1 of corporate finance assignment
Option B (Mean: 0.1285 and Standard deviation: 0.18541)
Answer 2
a) In order to determine which project the company must choose, the NPV (Net Present Value) of each of the two projects needs to be determined. NPV (Project A) = -$100 million + ($18 million/0.1) = $80 million NPV (Project B) = -$100 million + ($12 million/(0.1-0.04)) = $100 million Since the NPV of project B exceeds that of project A, hence project A would be preferred over project B.

b) IRR is defined as the discount rate for which NPV becomes zero.
The IRR for project A is computed below.
$100 million = ($18million/(1+r))
Solving the above, r = 18%
Hence, IRR for project A is 18%.

The IRR for project B is computed below.
$100 million = $12million/(r%-0.04)

Solving the above, r = 16%
Hence, IRR for project B is 16%.

Answer 3
In order to determine the bank which is offering the best rate, it is imperative to determine the Effective Annual Rate (EAR) for each of the banks.

EAR (Bank A) = 10%
EAR (Bank B) = (1+ (9.8%/2))2 -1 = 10.04% EAR (Bank C) = (1+ (9.6%/4))4-1 = 9.95%
EAR (Bank D) = (1+ (9.5%/12))12-1 = 9.92%
EAR (Bank E) = (1+ (9.4%/365))365 -1 = 9.85%

From the above computation, it is evident that the best rate is being offered by Bank B.

Total amount at the end of 20 years with bank E = $150,000*(1+ (9.4%/365))365*20 = $982,788
Total amount at the end of 20 years with bank B = $150,000 *(1 + (9.8%/2))2*20 = $1,016,508 Difference in interest earned = $1,016,508 -$982,788 = $33,720

Answer 4
The free cash flows of the company from the year 1 to year 3 are estimated as follows.

FCF (Year 1) = 150*(1-0.4) + 25 – 50 = £65 million
FCF (Year 2) = 180*(1-0.4) + 30 – 75 = £63 million
FCF (Year 3) = 200*(1-0.4) + 30 – 85 = £65 million

Terminal value of FCF (Year 4 onwards) = £65 million*(1+5%)/(10%-5%) = £1,365 million

The value of the corporation would be the present value of all the future FCF.

Hence, value of corporation = (65/1.1) + (63/1.12) + (65/1.13) + (1,365/1.13) = £1,185.54 million

Answer 5
a) The current price of the bond would be equal to the present value of all the expected future cash inflows.

Face value = $1,000
Coupon rate = 7%
Coupon Amount = $1,000*7% = $ 70
Maturity period = 5 years
Expected returns = 8%

Hence, current price of bond = 70/1.08 + 70/1.082 + 70/1.083 + 70/1.084 + 1070/1.085 = $960.07
b) Coupon rate of bond = ($95/$1000) = 9.5% p.a. YTM = ?

Current price of bond = $1.087.75 Maturity period = 25 years
Hence, 1087.75 = PV of coupon payments + PV of face value repayment
PV of coupon payments = $95*(1-(1+YTM)-25)/(1+YTM)
PV of face value repayment = $1000/(1+YTM)25
Thus, 1087.75 = $95*(1-(1+YTM)-25)/(1+YTM) + $1000/(1+YTM)25
Solving the above, YTM = 8.63% p.a.

Answer 6
a) Let x% of the portfolio be invested in risky assets 0.18*x% + 0.07*(100-x%) = 0.15
Solving the above, x = 72.72%

b) The amount invested in risky asset = 72.72%*$150,000 = $109,091
c) The standard deviation of a riskless asset would be zero. Hence, the standard deviation of the portfolio would essentially be the weight of risky asset multiplied by the corresponding standard deviation.
Hence, standard deviation of portfolio = 72.72%*0.2 = 0.145

Answer 7
a) Expected return on debt = 2% +0.2*5% = 3% p.a.
Expected return on equity = 2% + 1.3*5% = 8.5% p.a.
b) After-tax cost of debt = 3%*(1-0.25) = 2.25%p.a.
Weight of debt = 200/(320+200) = 0.3846
Weight of equity = 320/(320+200) = 0.6154
After tax WACC at the current leverage = 0.3846*2.25% + 0.6154*8.5% = 6.10% p.a.