Question

There are two risky investments, Chaser and Steady.

Chaser has two equally likely possibilities both with perpetual cash flows. It can have either a good state or a bad state. In the good state, cash flows start at £15m at the end of year one and grow at the rate of 4% every year while in the bad state, cash flows start at £12m at the end of year one and decline at the rate of 2% every year.

The cash flows of Steady will start at £24m at the end of the fourth year and remain at that level forever.

As a measure of the risk in each project the relevant beta of Chaser is 1.5 and of Steady is 0.5. The current base rate (i.e. risk free rate) is 3% per annum and the expected stock market return is 9% per annum.

The investment costs are £98m for Chaser and £284m for Steady.

1. a) Which investment should be preferred according to the Net Present Value criteria?

2. b) If you could shut down the Chaser investment when the bad state occurs at zero cost, which investment should be preferred according to the Net Present Value criteria?

3. c) A large multinational is willing to buy the Chaser investment at any time. You are negotiating the price they should pay for it. What is the minimum price you must bargain for to ensure the Chaser investment is worth more than the Steady investment?

Answer 1

Cost of Equity
CAPM	Rf+Beta*(Rm-Rf)
Rf	3%
Rm	9%
Beta Chaser	1.5
Cost of equity Chaser	12%
Beta Steady	0.5
Cost of equity Steady	6%
Chaser	Good State	Bad State
Investment costs	-98	-98
Initial cash flows	15	12
Growth rate	4%	-2%
Perpetual cash flows	195	84	<--Initial cash flow*(1+growth rate)/(Cost of equity-growth rate)
Probability of happening	50%	50%
Weighted cash flows of chaser	97.5	42	139.5	<--Sum(195*50%+84*50%)
Net Present value	41.5	<--139.5-98
Steady
Investment costs	-284
Initial cash flows	24
Growth rate	0
Perpetual cash flows	400
Net Present value	116	<--400-284

a) As per NPV criterio Steady should be choosen

b) Chaser in bad state NPV=84-98=-14

Excluding this, value of chaser only comes from good state=97.5*50%=48.5

Still, steady gives better NPV thus it should be choosen

c) The minimum price should be equal to the NPV of steady atleast

Please reach out for any clarifications