Question

Capital Budgeting Methods Project S has a cost of $10,000 and is expected to produce benefits (cash flows) of $3,000 per year for 5 years. Project L costs $25,000 and is expected to produce cash flows of $7,300 per year for 5 years. Calculate the two projects' NPVs, assuming a cost of capital of 12%. Round your answers to the nearest cent. Project S $ Project L $ Which project would be selected, assuming they are mutually exclusive? Calculate the two projects' IRRs. Round your answers to two decimal places. Project S % Project L % Which project would be selected, assuming they are mutually exclusive? Calculate the two projects' MIRRs, assuming a cost of capital of 12%. Round your answers to two decimal places. Project S % Project L % Which project would be selected, assuming they are mutually exclusive? Calculate the two projects' PIs, assuming a cost of capital of 12%. Round your answers to two decimal places. Project S Project L Which project would be selected, assuming they are mutually exclusive? Which project should actually be selected?

Answer 1

NPV of Project S = -10000 + 3000/(1+0.12) + 3000/(1+0.12)^2 + 3000/(1+0.12)^3 + 3000/(1+0.12)^4 + 3000/(1+0.12)^5 = 814.3286

NPV of Project L = -25000+ 7300/(1+0.12) + 7300/(1+0.12)^2 + 7300/(1+0.12)^3 + 7300/(1+0.12)^4 + 7300/(1+0.12)^5 = 1314.866

As NPV of Project L > NPV of Project S, Project L should be selected.

We know IRR is the Discount rate at which the NPV turns out to be 0.

Therefore, for Project S,

-10000 + 3000/(1+IRR) + 3000/(1+IRR)^2 + 3000/(1+IRR)^3 + 3000/(1+IRR)^4 + 3000/(1+IRR)^5 = 0

By making various substitutions in above equation we get,

IRR = 15.27%

For Project L,

-25000+ 7300/(1+IRR) + 7300/(1+IRR)^2 + 7300/(1+IRR)^3 + 7300/(1+IRR)^4 + 7300/(1+IRR)^5 = 0

By making various substitutions in above equation we get,

IRR = 14.1%

As IRR of Project S > IRR of Project L, Project S should be selected.

For Project S, Furture Value of all cash Inflow = 3000*(1+0.12)^0 + 3000*(1+0.12)^1 + 3000*(1+0.12)^2 + 3000*(1+0.12)^3 + 3000*(1+0.12)^4 = 19058.54

MIRR = Sqrt(FV of all inflow/Initial Investment) - 1 =  Sqrt(19058.54/10000) - 1 = 0.3805 = 38.05%

For Project L, Furture Value of all cash Inflow = 7300*(1+0.12)^0 + 7300*(1+0.12)^1 + 7300*(1+0.12)^2 + 7300*(1+0.12)^3 + 7300*(1+0.12)^4 = 46375.79

MIRR = Sqrt(FV of all inflow/Initial Investment) - 1 =  Sqrt(46375.79/25000) - 1 = 0.362 = 36.2%

As MIRR of Project S > MIRR of Project L, Project S should be selected.

Profitability Index of Project S = (NPV of S + Initial Investment)/Initial Investment = (814.3286+10000)/10000 = 1.0814

Profitability Index of Project L = (NPV of L + Initial Investment)/Initial Investment = (1314.866+25000)/25000 = 1.0525

As PI of Project S > PI of Project L, Project S should be selected.

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