Question

Consider two projects, A and B. Project A's first cash flow is $10,500 and is received three years from today. Future cash flows for Project A grow by 4 percent in perpetuity. Project B's first cash flow is −$9,200, which occurs two years from today, and will continue in perpetuity. Assume that the appropriate discount rate is 12 percent.

A) What is the present value of each project? (a negative answer should be indicated by a minus sign. Do not round intermediate calculations and round your answers to 2 decimal places.

Present Value

Project A $?

Project B $?

B) Suppose that the two project are combined into one project, called C. What is the IRR of Project C? (Do not round intermediate calculations and round your answers to 2 decimal places.)

IRR= ?%

C) What is the correct IRR rule for Project C?

-Accept the project if the discount rate is above the IRR

-Accept the project if the discount rate is equal the IRR

-Accept the project if the discount rate is below the IRR

Answer 1

Hello,

Here is the solution to your question -

a)

Project A

The first cash flow is at t=3 of $10500

Also from t = 4 onwards, cash flow grow by 4% till perpetuity. To calculate PV of this cash flow till perpetuity at t=2, use the following formula

PV_t=2 = FV/i-g

where FV = 10500

i = discount rate = 12%

g = growth rate = 4%

so, PV_t=2 = 10500/0.12-0.04 = $131250

So, Finally,

PV of Project A at t=0 = $131250 discounted at 12% over 2 years = 131250/(1.12)^2 = $104631.7

Project B

PV_t=1 = FV/i = -9200/0.12 = -$76666.67

So, finally,

PV of Project B at t=0 = - $76666.67 discounted at 12% for 1 year = - $68452.38

b) If both the projects are combined, then

NPV = PV of Project A + PV of Project B = 104631.7 - 68452.38 = $ 36179.32

c) The correct IRR rule for Project C is this -

Accept the project if the discount rate is below the IRR