Question

Games, Inc. is considering selling tennis racquets. It can use a proven technology to produce the racquets. This method will produce a $24M cashflow next year. The firm could also choose a new experimental method for producing racquets. This method has lower costs if it works. If the new technology works it will produce a cashflow of $28M next year. If it is unsuccessful it will produce a zero cashflow next year. The probability of success is 0.8 and the cashflows are uncorrelated with the market return. Both methods require a $20M dollar investment today. There are no cashflows after next year. The risk-free rate is 10%. The market price of risk is 8.4%.

1. (a) What is the NPV of the two projects? Which project should an all equity firm choose? Hint. You will have to determine the discount rate for both technologies [5 Marks]

2. (b) Games, Inc. has decided to raise $20M by issuing debt. The bondholders believe Games Inc’s assertion that they will use the old technology. (You could also assume that the bondholders have never heard about the new technology).

   What is the NPV of the equity if the old technology is chosen? What is the NPV of the equity if the new technology is chosen? Which project will shareholders choose? [5 Marks]

Answer 1

Given data, Initial Cash outflow = $ 20M

Cash inflow at next year (as per old technology) = $ 24M

Probable Cash inflow at next year (as per new technology) = $ 22.4M (Working Note-1)

Risk free rate of return = 10%

Market price risk = 8.4%

Risk Adjusted Discount Rate = 19.24% (Working Note-2)

Part (a):

OLD TECHNOLOGY-

Year Cash Flow [email protected] PVCF

0 ($ 20M) 1 ($ 20M)

1 $ 24M 0.839 $ 20.136M

Net Present Value (as per old technology) = $ 20.136M - $ 20M = $ 1.36M

NEW TECHNOLOGY-

Year Cash Flow [email protected]   PVCF

0 ($ 20M)    1 ($ 20M)

1 $ 22.4M   0.839 $ 18.7936M

Net Present Value (as per new technology) = $ 18.7936M - $ 20M = ($ 1.2064M)

Therefore, the probable cash inflow from the new technology incurs a negative net present value, so an equity firm should choose the old technology as it has a positive net present value.

Part (b):

Game Inc. wants to raise $ 20M by issuing debt

By problem, risk free rate = 10%

Hence, interest to be paid at next year on such debt = ($ 20M * 10% ) = $ 2M

OLD TECHNOLOGY-

Year Cash Flow   [email protected] PVCF

0 ($ 20M)   1 ($ 20M)

1 $ 24M - $ 2M = $ 22M 0.839 $ 18.458M

Net Present Value (as per old technology) = $ 18.458M - $ 20M = ($ 1.542M)

NEW TECHNOLOGY-

Year Cash Flow   [email protected]   PVCF

0 ($ 20M) 1 ($ 20M)

1 $ 22.4M - $ 2M = $ 20.4M 0.839 $ 17.1156M

Net Present Value (as per new technology) = $ 17.1156M - $ 20M = ($ 2.8844M)

Therefore, if the company issues debt to raise the initial fund, it would incur negative net present value in either of the technologies. Hence, in that case the shareholders will not choose any of the two given technologies as it would save at least a loss of $ 1.542M (i.e., minimum possible loss)

Working Note-1: Computation of probable cash inflow as per new technology

By problem, If the new technology works it will produce a cashflow of $28M next year. If it is unsuccessful it will produce a zero cashflow next year. The probability of success is 0.8

Hence, Probalility of earning $28M next year = 0.8

Probability of earning $0 next year = 0.2

Therefore, probable cash inflow at next year (as per new technology) = [($28M*0.8) + ($0*0.2)] = $ 22.4M

Working Note-2: Computation of Risk Adjusted Discount Rate (or, RADR)

We know, (1+RADR) = (1+Risk free rate) (1+Market risk percentage)

Or, (1+RADR) = (1+0.10) (1+0.084)

Or, (1+RADR) = 1.1924

Or, RADR = 1.1924 - 1

Hence, RADR = 0.1924 or 19.24%

Notes:

1. PVIF = Present Value Interest Factor

2. PVCF = Present Value of Cash Flow