Question

Project A has cash flows of $4,000, $3,000, $0, and $3,000 for Years 1 to 4, respectively. Project B has cash flows of $2,000, $3,000, $2,000, and $3,000 for Years 1 to 4, respectively. Which one of the following statements is correct assuming the discount rate is positive? (No calculations needed)


a. The cash flows for Project B are an annuity, but those of Project A are not.
b. Both sets of cash flows have equal present values as of Time 0.
c. The present value at Time 0 of the final cash flow for Project A will be discounted using an exponent of three.
d. Both projects have equal values at any point in time since they both pay the same total amount.
e. Project B is worth less today than Project A.

Answer 1

Answer:

e. Project B is worth less today than Project A.

Explanation:

a. The cash flows for Project B are an annuity, but those of Project A are not.

FALSE because Cash flow of both project are not same in every years. An annuity pay fixed stream of payments.

b. Both sets of cash flows have equal present values as of Time 0.

FALSE

PV of project A = 4000/(1+rate)+3000/(1+rate)^2+0/(1+rate)^3+3000/(1+rate)^4

PV of project B = 2000/(1+rate)+3000/(1+rate)^2+2000/(1+rate)^3+3000/(1+rate)^4

To compare PV of 2 project, we omit same component and nil value, then if rate is positive, then it's clearly that

4000/(1+rate) > 2000/(1+rate) + 2000/(1+rate)^3

=> PV of project A > PV of project B

c. The present value at Time 0 of the final cash flow for Project A will be discounted using an exponent of three.

FALSE, Cash flow in Year 4 will use an exponent of four

d. Both projects have equal values at any point in time since they both pay the same total amount.

FALSE, as explained in item c. PV of project A > PV of project B

e. Project B is worth less today than Project A.

TRUE, as explained in item c. PV of project A > PV of project B