Question

Problem 16-3 Flounder Clinic is considering investing in new heart-monitoring equipment. It has two options. Option A would have an initial lower cost but would require a significant expenditure for rebuilding after 4 years. Option B would require no rebuilding expenditure, but its maintenance costs would be higher. Since the Option B machine is of initial higher quality, it is expected to have a salvage value at the end of its useful life. The following estimates were made of the cash flows. The company's cost of capital is 7% Initial cost Annual cash inflows Annual cash outflows Cost to rebuild (end of year 4) Salvage value Estimated useful life Option A Option B $175,000 $271,000 $72,100 $82,400 $29,300 $25,700 $48,700 $0 $0 $7,200 7 years 7 years Click here to view Py table. Compute the (1) net present value, (2) profitability Index, and (3) internal rate of return for each option. (Hint: To solve for internal rate of return, experiment with alternative discount rates to arrive at a net present value of zero.) (if the net present value is negative, use either a negative sign preceding the number e.o. -45 or parentheses e.g. (45). Round answers for present value and IRR to 0 decimal places, e... 125 and round profitability index to 2 decimal places, e.g. 12.50. For calculation purposes, use 5 decimal places as displayed in the factor table provided.) Net Present Value Profitability Index Internal Rate of Return Option A $ 96 Option B $

Answer 1

Hi,

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Question:

Answer:

Option A:

Initial cost = $175,000

Annual cash inflow = $72,100

Annual cash outflow = $29,300

CF = $42,800

Cost of rebuild (end of year 4) = $48,700

CF at 4th year = -$5,900

Salvage value = 0

Estimate useful life = 7 years

Cost of capital = 7%

NPV = -CF0 + CF1/(1+r)^1 + CF2/(1+r)^2 + CF3/(1+r)^3 +CF4/(1+r)^4 + CF5/(1+r)^5 + CF6/(1+r)^6 +CF7/(1+r)^n7

= -175,000+42,800/(1+7%)^1+42,800/(1+7%)^2 + 42,800/(1+7%)^3 + (-$5,900)/(1+7%)^4 +

42,800/(1+7%)^5 + 42,800/(1+7%)^6 +42,800/(1+7%)^7

= -175,000+42,800/(1.07)^1+42,800/(1.07)^2 + 42,800/(1.07)^3 + (-$5,900)/(1.07)^4 +

42,800/(1.07)^5 + 42,800/(1.07)^6 +42,800/(1.07)^7

= -175,000+42,800/1.07 +42,800/1.1449 + 42,800/1.2250 + (-$5,900)/1.2862 +

42,800/1.3506 + 42,800/1.4181 +42,800/1.4890

= -175,000+ 40000 + 37383.17 + 34938.77 + (-4587.15) + 31689.61 + 30181.22 + 28744.12

= -175,000+ 198349.75 = $23349.74

NPV = $23350

IRR =  IRR is calculated using the same concept as NPV, except it sets the NPV equal to zero.

IRR = NPV =0 = -175,000+42,800/(1+10.01%)^1+42,800/(1+10.01%)^2 + 42,800/(1+10.01%)^3 + (-$5,900)/(1+10.01%)^4 + 42,800/(1+10.01%)^5 + 42,800/(1+10.01%)^6 +42,800/(1+10.01%)^7

=  -175,000+42,800/(1.1001)^1+42,800/(1.1001)^2 + 42,800/(1.1001)^3 + (-$5,900)/(1.1001)^4 + 42,800/(1.1001)^5 + 42,800/(1.1001)^6 +42,800/(1.1001)^7

= -175,000+42,800/1.1001 + 42,800/1.2102 + 42,800/1.3313 + (-$5,900)/1.4646+ 42,800/1.6112+ 42,800/1.7725 +42,800/1.9499

= -175,000+ 38905.55 + 35366.05 + 32149.02 + (-4028.40) + 26564.05 + 24146.68 +21949.84

IRR = NPV =0 = -175,000 + 175,052  (approx zero)

IRR = 10.01% or 10%

Profitability Index = Present value of future cash flow/initial investment

= $23350/ 175,000 = $ 0.1334

Profitability Index = $ 0.1334

Option B:

Initial cost = $271,000

Annual cash inflow = $82,400

Annual cash outflow = $25,700

CF = $56,700

Cost of rebuild (end of year 4) = $48,700

CF at 4th year = -$0

Salvage value = $7,200

Estimate useful life = 7 years

Cost of capital = 7%

NPV = -CF0 + CF1/(1+r)^1 + CF2/(1+r)^2 + CF3/(1+r)^3 +CF4/(1+r)^4 + CF5/(1+r)^5 + CF6/(1+r)^6 +CF7/(1+r)^n7

= -271,000+$56,700/(1+7%)^1+$56,700/(1+7%)^2 + $56,700/(1+7%)^3 + $56,700/(1+7%)^4 +

$56,700/(1+7%)^5 + $56,700/(1+7%)^6 + $56,700+7,200/(1+7%)^7

= -271,000+$56,700/(1.07)^1+ $56,700/(1.07)^2 + $56,700/(1.07)^3 + $56,700/(1.07)^4 +

$56,700/(1.07)^5 + $56,700/(1.07)^6 + 63900/(1.07)^7

= -271,000+$56,700/1.07 + $56,700/1.1449 + $56,700/1.2250 + $56,700/1.2862 +

$56,700/1.3506 + $56,700/1.4181 + 63900/1.4890

= -271,000+ 52990.65 + 49523.97 + 46285.71 + 44083.34 + 41981.34 + 39983.07 + 42912.70

= -271,000 + 317760.78 = $46760.78

NPV = $46760.78 or $46761

IRR = NPV =0 = - $271,000+ 56700/(1+10.96%)^1+56700/(1+10.96%)^2 + 56700/(1+10.96%)^3 + 56700/(1+10.96%)^4 + 56700/(1+10.96%)^5 + 56700/(1+10.96%)^6 + 63900/(1+10.96%)^7

= -$271,000+ 56700/(1.1096)^1+ 56700/(1.1096)^2 + 56700/(1.1096)^3 + 56700/(1.1096)^4 + 56700/(1.1096)^5 + 56700/(1.1096)^6 +63900/(1.1096)^7

= - $271,000 + 56700/1.1096 + 56700/1.2312 + 56700/1.3661 + 56700/1.5158+ 56700/1.6820 + 56700/1.8663 + 63900/2.0709

= - $271,000 + 51099.49 + 46052.63 + 41505.01 + 37405.99 + 33709.86 + 30380.96 + 30856.14

IRR = NPV =0 = -$271,000 + 271,010 (approx zero)

IRR = 10.96% or 11%

Profitability Index = Present value of future cash flow/initial investment

= $46760.78/ $271,000 = $0.1725

Profitability Index = $0.1725

Here i will select option B because the NPV, IRR and Profitability Index of option B is better than option A.

Thank You