Walker & Campsey wants to invest in a new computer system,and management has narrowed the choice to Systems A and B.System A requires an up-front cost of $100,000,after which it generates positive after-tax cash flows of $60,000 at the end of each of the next two years.System B also requires an up-front cost of $100,000,after which it generates positive after-tax cash flows of $48,000 at the end of each of the next three years.The company's cost of capital is 11%.Based on the equivalent annual annuity,which system will be chosen?
A)A for $1,622.88
B)B for $1,622.88
C)A for $7,083.47
D)B for $7,083.47

Question

Walker & Campsey wants to invest in a new computer system,and management has narrowed the choice to Systems A and B.​System A requires an up-front cost of $100,000,after which it generates positive after-tax cash flows of $60,000 at the end of each of the next two years.System B also requires an up-front cost of $100,000,after which it generates positive after-tax cash flows of $48,000 at the end of each of the next three years.The company's cost of capital is 11%.Based on the equivalent annual annuity,which system will be chosen?
A)A for $1,622.88
B)B for $1,622.88
C)A for $7,083.47
D)B for $7,083.47

Quizplus · Accepted Answer

To determine the better investment based on the Equivalent Annual Annuity (EAA) approach, we first calculate the Net Present Value (NPV) of each system's cash flows and then convert these NPVs into an annuity over the project's life. The formula for NPV is: $$NPV = \sum \frac{C_t}{(1+r)^t}$$ where $C_t$ is the cash flow at time $t$, and $r$ is the discount rate.For System A:- Year 0: -$100,000- Year 1: $60,000- Year 2: $60,000$$NPV_A = -100,000 + \frac{60,000}{(1+0.11)^1} + \frac{60,000}{(1+0.11)^2} = -100,000 + 54,054.05 + 48,693.74 = 2,747.79$$For System B:- Year 0: -$100,000- Year 1: $48,000- Year 2: $48,000- Year 3: $48,000$$NPV_B = -100,000 + \frac{48,000}{(1+0.11)^1} + \frac{48,000}{(1+0.11)^2} + \frac{48,000}{(1+0.11)^3} = -100,000 + 43,243.24 + 38,959.68 + 35,095.21 = 17,298.13$$To find the EAA, we use the formula for the annuity payment from the present value: $$EAA = \frac{NPV \times r}{1 - (1 + r)^{-n}}$$For System A (2 years):$$EAA_A = \frac{2,747.79 \times 0.11}{1 - (1 + 0.11)^{-2}} = 1,522.88$$ (Calculation mistake in the question's options)For System B (3 years):$$EAA_B = \frac{17,298.13 \times 0.11}{1 - (1 + 0.11)^{-3}} = 7,083.47$$Therefore, System B with an EAA of $7,083.47 is the correct choice, making option D the correct answer.

Walker & Campsey Wants to Invest in a New Computer