Question

1.Your factory has been offered a contract to produce a part for a new printer. The contract would last for three​ years, and your cash flows from the contract would be

$ 4.94 million per year. Your upfront setup costs to be ready to produce the part would be $ 7.98 million. Your discount rate for this contract is 7.7 %

a. What is the​ IRR?

b. The NPV is $ 4.82 million, which is positive so the NPV rule says to accept the project. Does the IRR rule agree with the NPV​ rule?

2.You are considering making a movie. The movie is expected to cost $10.0 million up front and take a year to produce. After​ that, it is expected to make $5.0 million in the year it is released and $2.0 million for the following four years. What is the payback period of this​ investment? If you require a payback period of two​ years, will you make the​ movie? Does the movie have positive NPV if the cost of capital is 10.0%​?

3.

The Jones Company has just completed the third year of a​ five-year MACRS recovery period for a piece of equipment it originally purchased for $295,000.

a. What is the book value of the​ equipment?

The book value of the equipment after the third year is $

b. If Jones sells the equipment today for $179,000 and its tax rate is 35%​, what is the​ after-tax cash flow from selling​ it?

Note​: Assume that the equipment is put into use in year 1.

Answer 1

1.

Initial investment = $ 7.98 million.

Cash flow per year = $ 4.94 million per year for 3 years.

a) IRR will be calculated using hit and trial approach.

IRR of a proposal is defined as the discount rate at which NPV is 0. It is the rate at which the present value of cash inflows is equal to present value of cash outflows.

Suppose required rate of return (K) = 38 %. Present value of cash inflow will be calculated using below formula-

For ex-

Present value of cash inflow for 2nd year will be =

= $ 2.593992859 million

year	cash inflow (in million $)	present value of cash inflow
1	4.94	3.579710145
2	4.94	2.593992859
3	4.94	1.87970497

NPV = Present value of all years cash inflows - present value of cash outflows.

NPV at 38 % discount rate = 8.053 - 7.98

= 0.073 million $ (approx)

Now suppose, K = 39 %

year	cash inflow(in million $)	present value of cash inflow
1	4.94	3.553956835
2	4.94	2.556803478
3	4.94	1.839426963

NPV at 39 % discount rate = 7.950 - 7.98

= - 0.03 million $

where ,
L = Lower discount rate at which NPV is positive.
H = Higher discount rate at which NPV is negative.
A = NPV at lower discount rate.
B = NPV at higher discount rate.

= 38.71 % (approx)

IRR = 38.71 %

Discount rate for this contract = 7.7 % (given)

Decision rule for IRR - "Accept the project in which the IRR is greater than cost of capital and reject where IRR is less than cost of capital."

Here IRR is greater than the discount rate/cost of capital, hence the project should be accepted.

Also, the IRR rule agrees with NPV rule.

Hope it helps!