Use the following for Questions 1 - 4: You are considering two mutually exclusiv

Question

Use the following for Questions 1 - 4:

You are considering two mutually exclusive projects, A and B.

Project A costs $70,000 and generates cash flows of $12,000 for 10 years.

Project B costs $60,000 and generates cash flows of $2,000 for six years and then cash flows of $29,000 for four years.

Report rates in percentage form to two decimal places i.e. 10.03% not 10%

Question 1

At what discount rate would make you indifferent between choosing one project or another?

Question 2

Which project would you ACCEPT if your discount rate was 10%?

A) Project A

B) Project B

C) Both Project A and B

D) Neither Project A or B

Question 3

Which project would you ACCEPT if your discount rate was 5%?

A) Project A

B) Project B

C) Both Project A and B

D) Neither Project A or B

Question 4

What is the highest discount rate in which you can still produce a non-negative NPV?

Explanation / Answer

Answer 1 Calculation of discount rate that would make you indifferent between choosing one project or another To find out this rate , we have to take difference of cash flows between two projects and then apply IRR formula to this difference. Year Cash flows Project A Project B Difference 0 -70000 -60000 -10000 1 12000 2000 10000 2 12000 2000 10000 3 12000 2000 10000 4 12000 2000 10000 5 12000 2000 10000 6 12000 2000 10000 7 12000 29000 -17000 8 12000 29000 -17000 9 12000 29000 -17000 10 12000 29000 -17000 IRR of cash flow difference = 7.47% Discount rate that would make you indifferent between choosing one project or another = 7.47% Answer 2 We decide about the projects based on NPV.The project with higher NPV will be selected. Year Discount factor @ 10% Project A Project B Cash flow Present Value Cash flow Present Value 0 1 -$70,000.00 -$70,000.00 -$60,000.00 -$60,000.00 1 0.909091 $12,000.00 $10,909.09 $2,000.00 $1,818.18 2 0.826446 $12,000.00 $9,917.36 $2,000.00 $1,652.89 3 0.751315 $12,000.00 $9,015.78 $2,000.00 $1,502.63 4 0.683013 $12,000.00 $8,196.16 $2,000.00 $1,366.03 5 0.620921 $12,000.00 $7,451.06 $2,000.00 $1,241.84 6 0.564474 $12,000.00 $6,773.69 $2,000.00 $1,128.95 7 0.513158 $12,000.00 $6,157.90 $29,000.00 $14,881.59 8 0.466507 $12,000.00 $5,598.09 $29,000.00 $13,528.71 9 0.424098 $12,000.00 $5,089.17 $29,000.00 $12,298.83 10 0.385543 $12,000.00 $4,626.52 $29,000.00 $11,180.76 NPV $3,734.81 $600.41 NPV of Project A $3,734.81 NPV of Project B $600.41 As NPV of project A is higher , it will be selected. The answer is Option A. Answer 3 We decide about the projects based on NPV.The project with higher NPV will be selected. Year Discount factor @ 5% Project A Project B Cash flow Present Value Cash flow Present Value 0 1 -$70,000.00 -$70,000.00 -$60,000.00 -$60,000.00 1 0.952381 $12,000.00 $11,428.57 $2,000.00 $1,904.76 2 0.907029 $12,000.00 $10,884.35 $2,000.00 $1,814.06 3 0.863838 $12,000.00 $10,366.05 $2,000.00 $1,727.68 4 0.822702 $12,000.00 $9,872.43 $2,000.00 $1,645.40 5 0.783526 $12,000.00 $9,402.31 $2,000.00 $1,567.05 6 0.746215 $12,000.00 $8,954.58 $2,000.00 $1,492.43 7 0.710681 $12,000.00 $8,528.18 $29,000.00 $20,609.76 8 0.676839 $12,000.00 $8,122.07 $29,000.00 $19,628.34 9 0.644609 $12,000.00 $7,735.31 $29,000.00 $18,693.66 10 0.613913 $12,000.00 $7,366.96 $29,000.00 $17,803.48 NPV $22,660.82 $26,886.63 NPV of Project A $22,660.82 NPV of Project B $26,886.63 As NPV of project B is higher , it will be selected. The answer is Option B. Answer 4 Calculation of highest discount rate in which you can still produce a non-negative NPV To find out this rate , we have to find out IRR for both projects. Year Cash flows Project A Project B 0 -70000 -60000 1 12000 2000 2 12000 2000 3 12000 2000 4 12000 2000 5 12000 2000 6 12000 2000 7 12000 29000 8 12000 29000 9 12000 29000 10 12000 29000 IRR = 11.23% 10.14% Highest discount rate for project A 11.23% Highest discount rate for project B 10.14%

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