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Problem 12:23 Comprehensive Problem (LO12-1, LO12-2, L012-3, LO12-5, LO12-6] ou Barlow, a divisional manager for Sage Company
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Answer #1

Solution

As per information provided,

Product A Product B
($) ($)
Initial Investment    2,50,000.00    4,60,000.00
Cash Flow After Tax
(CFAT):
Sales Revenue    3,00,000.00    4,00,000.00
Variable Expenses -1,35,000.00 -1,90,000.00
Depreciation      -50,000.00      -92,000.00
Fixed Cost      -75,000.00      -55,000.00
Net Cash Flow        40,000.00        63,000.00
Depreciation        50,000.00        92,000.00
CFAT        90,000.00    1,55,000.00

(1)

Payback Period
Product A Product B
(A) Initial Investment (in $)    2,50,000.00    4,60,000.00
(B) CFAT (in $)        90,000.00    1,55,000.00
Payback Period (in Years)
(A/B)                  2.78                  2.97

(2)

Net Present Value
Product A Product B
(A) Initial Investment 2,50,000.00 4,60,000.00
(B) CFAT      90,000.00 1,55,000.00
(C) Present Value Interest Factor of Annuity
for 5 years @ 18% (Refer table attached) 3.127 3.127
(D) Discounted CFAT (B x C) 2,81,430.00 4,84,685.00
(E) Net Present Value (D - A)      31,430.00      24,685.00

Present value of an ordinary) Annuity (PVIFA) Period 2% 3% 4% 5% 6% 7% 8% 0.990 0.971 0.9620.952 .943 09150 926 1.942 1913 19

(3)

Computation of Internal Rate of Return
Product A Product B
(A) Initial Investment 2,50,000.00 4,60,000.00
(B) CFAT      90,000.00 1,55,000.00
At IRR, Discounted CFAT = Initial Outflow
So, Desired PVIFA (A/B)                 2.78                 2.97

For Product A, PVIFA for 5 Years 2.78 falls between 20% (PVIFA = 2.9906) and 24% (PVIFA = 2.7454),

(2.78 - 2.7454) / (2.9906 - 2.7454) = (X - 24) / (20 - 24)

Or, 0.0346 / 0.2452 = (24 - X) / 4

Or, 24 - X = 0.5644

Or, X = 24 - 0.5644

Or, X = 23.44 (Approx)

So, IRR for Product A = 23.44 %

For Product B, PVIFA for 5 Years 2.97 falls between 20% (PVIFA = 2.9906) and 24% (PVIFA = 2.7454)

(2.97 - 2.9906) / (2.7454 - 2.9906) = (X - 20) / (24 - 20)

Or, 0.0206 / 0.2452 = (X-20) / 4

Or, X - 20 = 0.3361

Or, X = 20 + 0.3361

Or, X = 20.34 (Approx)

So. IRR for Product B = 20.34 %

Table A-4 Present Value Interest Factors for a One-Dollar Annuity Discounted atk Percent for n Periods: PVIFA - (1 - 1/(1+k)

(4)

Project Profitability Index
Product A Product B
(A) Initial Investment 2,50,000.00 4,60,000.00
(B) CFAT      90,000.00 1,55,000.00
(C) Present Value Interest Factor of Annuity
for 5 years @ 18% (Refer table attached) 3.127 3.127
(D) Discounted CFAT (B x C) 2,81,430.00 4,84,685.00
(E) Project Profitability Index (D / A)                 1.13                 1.05

Present value of an ordinary) Annuity (PVIFA) Period 2% 3% 4% 5% 6% 7% 8% 0.990 0.971 0.9620.952 .943 09150 926 1.942 1913 19

(5)

Simple Rate of Return
Product A Product B
(A) Net Cash Flow      40,000.00      63,000.00
(B) Initial Investment 2,50,000.00 4,60,000.00
(C) Simple Rate of Return (in %) [(A/B) x 100]              16.00              13.70

(6a)

Measure Product A Product B Remarks
1. Payback Period 2.78 Years 2.97 Years Due to lower Payback Period, Product A will be preferred
2. Net Present Value $ 31,430.00 $ 24,685.00 Due to higher NPV, Product A will be preferred
3. Internal Rate of Return 23.44% 20.34% Due to higher IRR, Product A will be preferred
4. Project Profitability Index 1.13 1.05 Due to higher Project PI, Product A will be preferred
5. Simple Rate of Return 16% 13.70% Due to higher rate of return, Product A will be preferred

(6b)

Based on the Simple Rate of Return, Product A has higher rate of return than Product B. Hence Lou Barlow should prefer Product A over Product B.

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