Question

(a) The manufacturing firm Rebo is considering a new capital investment project. The project will last for five years. The anticipated sales revenue from the project is $3 million in year 1 and $4.2 million in each of years 2 – 5. The cost of materials and labour is 50% of sales revenue and other expenses are $1 million in each year. The project will require working capital investment equal to 20% of the expected sales revenue for each year. This investment must be in place at the start of each year. Working capital will be recovered at the end of the project’s life.

The project will require $2.5 million to be spent now on new machinery which will have zero value at the end of the project and will be depreciated each year at 20% of the original cost. The tax rate is 25%. Rebo uses a discount rate of 11% to evaluate its capital investment projects.

(i) What is the net income in each year?

(ii) What is the free cash flow in each year and the net present value (NPV)?

(iii)You discover the following additional information:

• The project will utilise a building that the firm leases. No other activities take place in it. If this project does not go ahead the firm will terminate the lease in one year’s time if no other use for it has been found.

• Part of each year’s cash flows from the project will be used to increase the dividend payment to shareholders.

For each of these items, explain briefly whether or not you would incorporate the information into your analysis of the project’s value.

(b) Zuti has a capital investment project that could start immediately. The project will require a machine costing $2.4 million. The total discounted value now of the cash inflows from the project will be either $2.6 million or $1.9 million with equal probability. The risk-free rate is 3%.

Instead of starting immediately the project could be delayed until one year from now to gain more market information. Its total discounted cash inflows at that time will be known as either $2.6 million, or $1.9 million, with certainty.

(i) What is the present value of the option to delay?

(ii) The supplier of the machine has offered to deliver it (if required) in one year’s time at a price of only $2 million, if Zuti pays a non-refundable deposit now. What is the maximum the firm should pay as a deposit now? What type of real option does this represent for Zuti? Identify the specific components of the option contract.

Answer 1

b)

Present value of the option to delay

Value of a call option = P_a*N(d_1) - P_e*N(d_2)*e^{-rt}

where,

d_1 = \frac{ln(P_a/P_e)+(r+0.50s^2)*t}{s\sqrt{t}}

d_2 = d_1-{s\sqrt{t}}

Pa = $2.6M*50%+$1.9M*50% = $2.25M]

here, cost of asset, Pe = $2.40M

d1 = [ln($2,250,000/$2,400,000)+(0.30+0.50*(0.50)2)*1]/(0.50*1)]

= [ln(0.9375)+0.425]/0.50

= [-0.0280+0.425]/0.50

= 0.794

= 0.79

d2 = 0.794- (0.50*1) = 0.294 = 0.29

N(d1) = 0.50+0.2852 = 0.7852 ;

N(d2) = 0.50+0.1141 = 0.6141

Value of call option = [$2,250,000*0.7852]-[$2,400,000*0.6141*2.7183(-0.03*1)]

= $1,766,700 - $1,473,840*0.9705

= $1,766,700 - $1,430,362 = $336,338

We first compute the values for N(d1) and N(d2) as below -

d1 = [ln($2,000,000/$2,400,000)+(0.30+0.50*(0.50)2)*1]/(0.50*1)]

= [ln(0.8333)+0.425]/0.50

= [-0.0792+0.425]/0.50

= 0.6916

= 0.69

d2 = 0.6916- (0.50*1)

= 0.1916

= 0.19

N(d1) = 0.50+0.2549 = 0.7549 ;

N(d2) = 0.50+0.0753 = 0.5753

Then, value of call option can be computed as

Value of call option =

[$2,000,000*0.7549-[$2,400,000*0.5753*2.7183(-0.03*1)]

= $1,509,800 - $1,380,720*0.9705

= $1,509,800 - $1,339,989

= $169,811

Thus, Zuti should pay a maximum security deposit of $169,811.

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