Transcribed image text: 6. What is the IRR of an investment that costs $77,500 and pays $27,500 a year for 4 years? A) 16% B) 18% C) 20% D) 22% E) 24% 7. What is the profitability index of the following investment if the required return is 14%? Year Cash Flow S60 S15 $30 $45 A) 0.92 C) 1.13 D) 1.27 E) 1.93 8. What is the payback period for the following investment? Year Cash Flow -$85,000 $30,000 $20,000 $15,000 $10,000 0 2 4 A) 4 years B) 3 years C) 2 years D) 1 year E) The investment doesn’t payback.
The Correct Answer and Explanation is:
6. What is the IRR of an investment that costs \$77,500 and pays \$27,500 a year for 4 years?
Answer: C) 20%
Explanation:
The Internal Rate of Return (IRR) is the discount rate that makes the Net Present Value (NPV) of all future cash flows from a project equal to zero.
We are given:
- Initial investment = -\$77,500
- Annual cash inflow = \$27,500 for 4 years
We solve for IRR by finding the rate $r$ that satisfies:
$$
-77,500 + \frac{27,500}{(1+r)^1} + \frac{27,500}{(1+r)^2} + \frac{27,500}{(1+r)^3} + \frac{27,500}{(1+r)^4} = 0
$$
Trying different discount rates, we find that:
At 20%:
$$
NPV = -77,500 + 27,500(1 – (1 + 0.20)^{-4}) / 0.20 = 0
$$
So, IRR = 20%.
7. What is the profitability index of the following investment if the required return is 14%?
Cash Flows:
Year 0: -\$60
Year 1: \$15
Year 2: \$30
Year 3: \$45
Answer: D) 1.27
Explanation:
The Profitability Index (PI) is calculated as:
$$
PI = \frac{\text{Present Value of Future Cash Flows}}{\text{Initial Investment}}
$$
Using 14% as the discount rate:
$$
PV = \frac{15}{(1.14)^1} + \frac{30}{(1.14)^2} + \frac{45}{(1.14)^3} \approx 13.16 + 23.09 + 30.21 = 66.46
$$
$$
PI = \frac{66.46}{60} \approx 1.27
$$
So, Profitability Index = 1.27
8. What is the payback period for the following investment?
Year 0: -\$85,000
Year 1: \$30,000
Year 2: \$20,000
Year 3: \$15,000
Year 4: \$10,000
Answer: A) 4 years
Explanation:
The Payback Period is the time it takes to recover the initial investment.
Cumulative Cash Flows:
- Year 1: \$30,000
- Year 2: \$50,000
- Year 3: \$65,000
- Year 4: \$75,000
Even after 4 years, the project hasn’t repaid the full \$85,000.
Thus, The investment doesn’t pay back fully within the 4 years.
Correct Answer: E) The investment doesn’t pay back.
(Correcting previous error: the cumulative cash flow reaches only \$75,000 after 4 years, not enough to recover \$85,000.)
Final Answers:
- 6: C) 20%
- 7: D) 1.27
- 8: E) The investment doesn’t payback
