Question

Consider a hypothetical economy that has NO tax.

ABC Ltd. is considering investing in a 2-year project which is expected to generate the following year-end cash flows: C1 = $110 million, C2 = $115 million. The yearly discount rate for the project is 10%. The initial cost of the project is $200 million.

(e) Write down the numerical formula for computing the IRR of this project. What is the minimum IRR value that would make this project acceptable? Explain.

Given the recommendations based on the four decision rules above, which project should ABC Ltd. accept?

(f) Now suppose that of the $200m initial expenditure, $50m was used for the purchase of a machine that has an estimated economic life of four years. The machine will be fully depreciated (i.e., zero book value at the end of the machine’s economic life) on a straight-line basis and expected to have a resale value of $35m at the end of the project.

(i) Explain how this will affect the size of the terminal (end-of-project) cash flows.

(ii) How will this affect the NPV and the acceptance/rejection of the project (as compared to part (a))? Show your calculations.

Answer 1

-200+110/(1+r)+115/(1+r)^2=0
Let 1/(1+r) be x
-200+110x+115x^2=0
=>x=-1.8811,0.92454
=>x=0.92454
=>1/(1+r)=0.92454
=>r=8.161%

IRR=8.16%

Project will acceptable at an IRR of 8.16%.Hence Do not accept the project.

Step 1: Calculation of NPV without the salvage value:

Initial cost of the project	200,000,000	(A) = Given in question
Cash flow in year 1	110,000,000	(B) = Given in question
Cash flow in year 2	115,000,000	(C) = Given in question
Discount rate	10%	(D) = Given in question
Discount factor for year 1	0.909	(E) = 1/(1+(D))^1
Discount factor for year 2	0.826	(F) = 1/(1+(D))^2
Calculation of Net Present Value
Discounted Cash flow in year 1	100,000,000	(G) = (B)*(E)
Discounted Cash flow in year 2	95,041,322	(H) = (C)*(F)
Initial cost of the project	(200,000,000)	(A)
Net Present Value	(4,958,678)	(I) = (G)+(H)-(A)

Project has a negative Net Present Value of $4,958,678 and hence project should be rejected.

Step 2: If machine has resale value of $35M at end of year 2

Resale value of machine	35,000,000	(J) = Given in question
Discounted Resale value of machine in year 2	28,925,620	(K) = (J)*(F)

Present Value of resale value of $35M at end of year 2 is $28,925,620 and thus terminal cash-flow increases by $28,925,620 (answer to (i) )

Step 3: Calculation of revised NPV considering the resale value

Net Present Value without considering the resale value = -$4,958,678

Present Value of resale value = $28,925,620

Revised Net Present Value = -$4,958,678+$28,925,620 = $23,966,942

Resale value positively affects the NPV by making it as positive $23,966,942. Since NPV is positive now, project can be accepted ((answer to (ii) ).