MN30211, Advanced Corporate Finance.

Revision of BBA2 Corporate Finance MN20009.

1. A firm is considering investing in a project with the following cashflows. The firm has a cost of capital of 10%.

0 / 1 / 2 / 3 / 4 / 5
-1000 / 600 / 300 / 200 / 150 / 150

Calculate the NPV. Should the project be taken?

2. A firm is considering investing in a new 5 year project. The new project will require initial investment of £300,000, depreciated on a straight line basis. There is corporation tax of 25%.

The project will result in the following incremental cashflows per annum.

Units / Price/Unit
Revenue / 100,000 / £2
Direct Labour / 5 units produced per manhour / £4 per manhour
Direct Materials / 100,000 / £0.10

In addition, the project will attract £4 per unit of existing overheads. The firm has just undertaken a feasibility study for this project, costing £5000. The firm has a cost of capital of 12%.

What is the NPV of the project? Should the project be taken?

  1. A firm is considering the following mutually exclusive projects.

YEAR / A / B / C
0 / -1000 / -1000 / -1000
1 / 400 / 200 / 250
2 / 600 / 300 / 250
3 / 200 / 500 / 250
4 / -300 / 300 / 250
5 / -400 / 300 / 250
IRR / -50% / 20% / 25%

a)Calculate the NPV of each project, given that the cost of capital is 10%.

b)Calculate the paybacks of each project.

c)Compare the IRRs, NPVs, and paybacks and comment.

d)Which project should be taken? Justify your choice of decision rule.

e)Why may NPV and IRR give different decisions?

  1. A firm is appraising a new investment, requiring initial outlay of £900. It is expected to provide annual revenue of £1000, with annual variable costs equal to 60% of revenue, and annual fixed cost of £300, every year forever. Calculate the NPV, given a discount rate of 10%.
  1. Sketch a risk-averse investor’s utility of wealth function.
  1. The stock market consists of two shares (!). Share A has an expected return of 10%, and a standard deviation of 15%. Share B has an expected return of 15%, and a standard deviation of 20%. Sketch the investor’s opportunity set, and identify the efficiency frontier.
  2. Now the stock market contains many shares. On your previous diagram, add some inefficient portfolios. Why are they described as inefficient?

This economy also has a risk-free asset of 5% . Sketch the capital market line.

On your diagram, identify the market portfolio. Which portfolio should all risk averse investors hold? In holding this portfolio, which risk has been elminated, and which risk remains?

  1. An all equity firm is considering a new one-period project which will require investment of £1000 at the beginning of the period, and provide an expected income at the end of the period of £1150.

The expected return on the market equals 10%, and the risk-free rate equals 5%. Should the firm take the new project if

i)Beta = 1.0

ii) Beta = 1.5

iii)Beta = 2.0?

iv)Beta =2.5?

What is the NPV and in which direction does the share price move when the project is taken in each of these cases?

  1. Option Pricing: A firm’s shares are currently trading at £25 per share. The firm also issues one period call options (ie the exercise date is in one period’s time), with an exercise price of £30. In one period’s time, the share price will either increase to £35, or fall to £10, each with a probability of 0.5. The risk free rate is 10%. Using the binomial pricing model, what is the current price of the call option?

i)Buy 3 call options at a price of C each. (Hint: If you buy 1 call option, you gain £1 for every £1 that the share price exceeds the exercise price, so the slope of the line is 45%. What do you gain, and what is the slope of the line, if you buy 3 call options?)

ii) Sell 2 call options.

iii)Sell a call option and buy a put option.

iv)Buy a call option and sell 3 put options.

v)A long position in a share, with a short position in 2 calls.

vi)The option identity is S + P = B + C. What does this tell you about combining options to gain a risk-free profile? Use payoff profile diagrams to demonstrate this.

vii)You expect a firm’s shares to be extremely volatile. Demonstrate how you could combine a call and a put to gain for large changes in the stock price. What happens with small changes? What is this position called?

viii)You sell one call and sell one put. When do you gain, and when do you lose?