Question

4-1 You are considering three mutually exclusive design alternatives. Do nothing is also an option. MARR is 15%. A B Category First cost, $ Annual Expense, $/yr Annual revenue, $/yr Salvage value, $ Useful life, yrs ROR 26,000 12,500 20,000 5,000 10 26.60% 52,000 12,000 25,000 9,000 10 22.13% 40,000 21,000 29,000 8,000 10 16.30% a. What is the present worth of each alternative? Which would you choose? b. Perform an incremental analysis using present worth. Which would you choose? c. Perform an incremental analysis using rate of return. Which would you choose? [Calculate ROR to two decimal places (e.g., 6.78%) by manual interpolation. Show your factor notation and work.]

I only need help with doing Part C manually

Answer 1

The IRR of all the alternatives is greater than MARR thus, do nothing is rejected.

Alternative A has the lowest initial cost thus consider it as base alternative. Next best alternative is C. Determine the incremental cash flow that is C - A

The net present worth of the incremental cash flow is

$\large NPW_{C-A} = -14,000+ 500(P/A,i\%,10) + 3,000(P/F,i\%,10)$

Here the inflow in actual dollar is less than the outflow thus the incremental IRR will be negative. Thus, reject alternative C.

Next determine the incremental cash flow between A and B

$\large NPW_{B-A} = -26,000+ 5,500(P/A,i\%,10) + 4,000(P/F,i\%,10)$

Assume rate to be 17%

$\large NPW_{17\%} = -26,000+ 5,500(P/A,17\%,10) + 4,000(P/F,17\%,10)$

$\large \implies NPW_{17\%} = -26,000+ 5,500\times 4.6586+ 4,000\times 0.2080$

$\large \implies NPW_{17\%} = -26,000+ 25,622.32+ 832.15$

$\large \implies NPW_{17\%} = \$ \ 454.47$

Now assume rate to be 18%

$\large NPW_{18\%} = -26,000+ 5,500(P/A,18\%,10) + 4,000(P/F,18\%,10)$

$\large \implies NPW_{18\%} = -26,000+ 5,500\times 4.494 + 4,000\times 0.191$

$\large \implies NPW_{18\%} = -26,000+ 24,717.47 + 764.26$

$\large \implies NPW_{18\%} = -\$ \ 518.27$

Now apply linear interpolation

$\large \triangle _{B -A} = 17 + (18 -17)\times \frac{NPW_{17\%}}{NPW_{17\%}-NPW_{18\%}}$

$\large \triangle IRR_{B -A} = 17 + 1\times \frac{454.47}{454.47-(-518.27)}$

$\large \triangle IRR_{B -A} = 17 + 0.46$

$\large \triangle IRR_{B -A} = 17.46\%$

The incremental irr is greater than MARR thus select B and reject A.

Select B.

Refer the attached picture fir Excel calculation

В - А -26000 5500 5500 5500 А ТВ | с С-А -26000 Т-52000 Т-40000 Т-14000 7500 13000 8000 500 7500 | 13000 8000 500 7500 13000 8000 500 7500 13000 8000 500 7500 | 13000 | 8000 500 7500 13000 8000 500 7500 13000 8000 500 7500 Г 13000 8000 500 T 5500 5500 5500 5500 5500 9 17500 13000 18000 1500 15500 12500 22000 16000 3500 9500 | 26.60% | 22.13% | 16.30% 1 -7.16% | 17.46% IRR

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