Problem #1

Your company manufactures commercial cleaning equipment.You have the capacity to produce computer operated floor scrubbers. For this product line, model #1 will be produced for 10 years.However, if cash flows are higher than expected, model #2 will be introduced in the middle of year 3.If cash flows are higher than expected, model #3 will be introduced in the middle of year 5.You are being asked today to evaluate the proposal for creating the computer operated scrubbers.For both models 2 and 3, the introduction of the new product line will be a few months after the decision has been made. The hurdle return is 10% and the risk free rate is 5%.

You have the following information for Model #1:

The initial investment for model #1 is $10 million. Present value₀ today of 10 years of free cash flows is $22.7 million.

Information for Model #2:

The decision to introduce model #2 and terminate production of model #1 will be made at the start of year 3 using the cash flows from the first two years for model #1. The present value at start of year 3 is the sum of cash flows for next 7 years, netting cash flows no longer received from model #1 (cannibalized). PV₃ is $46 million. There is uncertainty about the forecasted cash flow, which may be 20% higher. The initial expenditure for production of model 2 will be made at the start of year 3, is known with certainty, and is $40 million.

Information for Model #3

The decision to introduction of model #3 and terminate production of model #2 will be made at the start of year 5 using the first two years cash flows for model #2. The present value at start of year 5 is the sum of cash flows for next 5 years, netting cash flows no longer received from model #2 (cannibalized). PV₅ is $71 million. There is uncertainty about the forecasted cash flow which may be 25% higher. The initial expenditure for production of model 3 will be made at the start of year 5 and is known with certainty and is $72 million.

1.Draw the decision tree for the problem with labels.

1.How much is the NPV of Model 1 alone?

2.Using the Black and Scholes excel, calculate value at year 3 of the call option to introduce Model 3.

3.How much is the market value of Model #2 with option to introduce Model #3?

4.Using the Black and Scholes excel calculate value the nested call option to introduce Model 2 with the possibility of replacing Model #2 with Model #3.

Model 3

Model #2 with possible Model 3

Market price (S)

Market price (S)

Strike price (K)

Strike price (K)

Time Years 5 to 3

Time Years 3 to 0

Percent higher

Percent higher

Interest rate

Interest rate

Call Price model 3

Price of nested call

.

5.How much is the net present value of model 1 with the option to replace Model #1 with Model #2 and the further possibility of replacing model #2 with Model #3?