Question

Water WorldWater World

is considering purchasing a water park in​ Atlanta, Georgia, for

$1,950,000.

The new facility will generate annual net cash inflows of

$481,000

for

eight

years. Engineers estimate that the facility will remain useful for

eight

years and have no residual value. The company uses​ straight-line depreciation, and its stockholders demand an annual return of

10​%

on investments of this nature.

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​(Click the icon to view Future Value of Ordinary Annuity of​ $1 table.)Read the requirements

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Requirement 1. Compute the​ payback, the​ ARR, the​ NPV, the​ IRR, and the profitability index of this investment.

​First, determine the formula and calculate payback. ​(Round your answer to one decimal​ place, X.X.)

Amount invested	/	Expected annual net cash inflow	=	Payback
	/		=		years

Answer 1

Answer :

1. Payback period :

= Amount invested / Expected annual net cash inflow

= $1,950,000 / $481,000

= 4 years

2. ARR :

Depreciation = $1,950,000 / 8 years = $243,750 per year

Return = Annual net cash inflow - Depreciation

= $481,000 - $243,750

= $237,250

ARR

= Return / Initial Investment x 100

= $237,250 / $1,950,000 x 100

= 12.2%

3. Net Present value :

= Present value of annual cash inflow - Amount invested

= [$481,000 x PVAF(10%,8years)] - $1,950,000

= [$481,000 x 5.33492] - $1,950,000

= $2,566,097 - $1,950,000

= $616,097

4. IRR :

IRR = R1  +  [NPV1 x (R2 - R1)] / (NPV1 - NPV2)

Where:

R1      =   Lower discount rate i.e 10%

R2      =   Higher discount rate i.e 15%

NPV1   =   Higher Net Present Value (derived from R1) i.e $616,097

NPV2   =   Lower Net Present Value (derived from R2)

= [$481,000 x PVAF(15%,8years)] - $1,950,000

= [$481,000 x 4.48732] - $1,950,000

= $208,401

IRR

= 10% + [$616,097 x (15 - 10)] / ($616,097 - $208,401)

= 10% + [$616,097 x5] / $407,696

= 10% + $3,080,485 / $407,696

= 10% + 7.6%

= 17.6% or 18%

5. Profitability index :

= Present value of annual cash inflow / Amount invested

= $2,566,097 / $1,950,000

= 1.3