Question

Wii Brothers, a game manufacturer, has a new idea for an adventure game. It can market the game either as a traditional board game or as an interactive DVD, but not both. Consider the following cash flows of the two mutually exclusive projects for the company. Assume the discount rate is 12 percent. Year Board Game DVD 0 –$ 1,200 –$ 2,700 1 690 1,750 2 950 1,570 3 210 800 a. What is the payback period for each project? b. What is the NPV for each project? c. What is the IRR for each project? d. What is the incremental IRR?

Answer 1

A) Payback period is the period of time taken by a project to recover its initial outflow.

i) BOARD GAME - Here, the initial outflow is $1200,

so the payback period shall be 1 year (to recover $690) + 0.537 years [(1200-690)/950] = 1.537 years.

ii) DVD - Here the initial outlay is $2700, so the period to recover the same shall be -

1 yr (to recover $1750) + 0.6051 yrs [(2700-1750)/1570] = 1.6051 years.

B) NPV (Net present value) = P.V. of inflows - P.V. of outflows

i) BOARD GAME -

P.V. of outflow = $1200

P.V. of inflow = 690/1.12 + 950/(1.12^2) + 210/(1.12^3) = $ 1522.879

NPV = 1522.879-1200 = $ 322.879

ii) DVD -

P.V. of outflow = $ 2700

P.V. of inflow = 1750/1.12 + 1570/(1.12^2) + 800/(1.12^3) = $ 3383.519

NPV = 3383.519-2700 = $ 683.519

C) IRR is essentially that rate at which P.V. of inflows equate with P.V. of outflows,

one of the methods to compute IRR is to use trial and error method to find the approximate rate and then using interpolation to arrive at the exact IRR. (another way is to directly use a financial calculator for the purpose, enter the cash flow details and IRR shall be readily available). Here we go for trial and error & interpolation -

i) BOARD GAME -

using discounting rate of say 29%,

we get P.V. of inflows to be = 690/(1.29)+950/(1.29^2)+210/(1.29^3) = $ 1203.588

This is quite close to the required amount of $ 1200 (which is the P.V. of outflow).

Now, using discounting rate of 30%,

we get P.V. of inflows to be = 690/(1.30)+950/(1.30^2)+210/(1.30^3) = $ 1188.484

Now we know that the required IRR is between 29% and 30% so we use interpolation to find the exact rate,

IRR = 29 + (1203.588-1200)/(1203.588-1188.484) = 29.2375%

Therefore, IRR = 29.2375%

ii) DVD -

using discounting rate of say 28%,

we get P.V. of inflows to be = 1750/(1.28)+1570/(1.28^2)+800/(1.28^3) = $ 2706.909

This is quite close to the required amount of $ 2700 (which is the P.V. of outflow).

Now, using discounting rate of 29%,

we get P.V. of inflows to be = 1750/(1.29)+1570/(1.29^2)+800/(1.29^3) = $ 2672.709

Now we know that the required IRR is between 28% and 29% so we use interpolation to find the exact rate,

IRR = 28 + (2706.909-2700)/(2706.909-2672.709) = 28.20%

Therefore, IRR = 28.20%

D) Incremental IRR - is the IRR found using the incremental cash flows (ie difference between the Cash flows of 2 projects)

Incremental outflow in the given case = $ 1500

Incremental inflow - Yr 1 $1060 ; Yr 2 $620; Yr 3 $590

using the trial and error and interpolation method, we find incremental IRR -

using discounting rate of say 28%,

we get P.V. of inflows to be = 1060/(1.28)+620/(1.28^2)+590/(1.28^3) = $ 1487.877

This is quite close to the required amount of $ 1500 (which is the P.V. of INCREMENTAL outflow).

Now, using discounting rate of 27%,

we get P.V. of inflows to be = 1060/(1.27)+620/(1.27^2)+590/(1.27^3) = $ 1507.079

Now we know that the required INCREMENTAL IRR is between 27% and 28% so we use interpolation to find the exact rate,

IRR = 27 + (1507.079-1500)/(1507.079-1487.877) = 27.36%

Therefore, INCREMENTAL IRR = 27.36%