Question

11. What is the internal rate of return for a project that requires a current cash outlay of $14,975 and is expected to generate cash inflows of $4,000 at the end of each of the next five years?
A. 10.1%
B. 10.5%
C. 11.0%
D. 11.5%
E. 12.0%

12. What is the internal rate of return for a project that requires a current cash outlay of $15,025 and is expected to generate cash inflows of $5,000 at the end of each of the next four years?
A. 11.5%
B. 12.0%
C. 12.5%
D. 13.0%
E. 14.1%

13. What is the internal rate of return for a project that requires a current cash outlay of $20,000 and is expected to generate cash inflows of 18% of the project cost for the next eight years?
A. 8.90%
B. 9.25%
C. 9.43%
D. 9.67%
E. 9.95%

Answer 1

Solution 11:

B. 10.5% is the answer.

Explanation

NPV = -14,975 + 4000/(1+IRR) + 4000/(1+IRR)^2+4000/(1+IRR)^3+4000/(1+IRR)^4+4000/(1+IRR)^5

At Internal Rate of return (IRR), Net Present value (NPV) equals zero

0 = -14,975 + 4000/(1+IRR) + 4000/(1+IRR)^2+4000/(1+IRR)^3+4000/(1+IRR)^4+4000/(1+IRR)^5

14,975 = 4000/(1+IRR) + 4000/(1+IRR)^2+4000/(1+IRR)^3+4000/(1+IRR)^4+4000/(1+IRR)^5

At IRR = 10%, PV = 15,163.15

At IRR = 11%, PV = 14,783.59

Using Interpolation to find IRR

10% + (15,163.15 - 14,975)/(15,163.15 - 14,783.59) x (11% - 10%)

10% + 0.50%

10.5%

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Solution 12:

C. 12.5% is the answer.

Explanation

NPV = -15,025+ 5000/(1+IRR) + 5000/(1+IRR)^2+5000/(1+IRR)^3+5000/(1+IRR)^4

At Internal Rate of return (IRR), Net Present value (NPV) equals zero

0 = -15,025 + 5000/(1+IRR) + 5000/(1+IRR)^2+5000/(1+IRR)^3+5000/(1+IRR)^4

15,025 = 5000/(1+IRR) + 5000/(1+IRR)^2+5000/(1+IRR)^3+5000/(1+IRR)^4

At IRR = 12%, PV = 15,186.75

At IRR = 13%, PV = 14,872.36

Using Interpolation to find IRR

12% + (15,185.75 - 15,025)/(15,186.75 - 14,872.36) x (13% - 12%)

12% + 0.50%

12.5%

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Solution 13:

A. 8.90% is the answer.

Explanation

Cash inflows = 18% of the project cost = 18%*20,000 = 3,600

NPV = -20000 + 3600/(1+IRR) + 3600/(1+IRR)^2+3600/(1+IRR)^3+3600/(1+IRR)^4+3600/(1+IRR)^5 + 3600/(1+IRR)^6 + 3600/(1+IRR)^7 + 3600/(1+IRR)^8

At Internal Rate of return (IRR), Net Present value (NPV) equals zero

0 = -20000 + 3600/(1+IRR) + 3600/(1+IRR)^2+3600/(1+IRR)^3+3600/(1+IRR)^4+3600/(1+IRR)^5 + 3600/(1+IRR)^6 + 3600/(1+IRR)^7 + 3600/(1+IRR)^8

20000 = 3600/(1+IRR) + 3600/(1+IRR)^2+3600/(1+IRR)^3+3600/(1+IRR)^4+3600/(1+IRR)^5 + 3600/(1+IRR)^6 + 3600/(1+IRR)^7 + 3600/(1+IRR)^8

At IRR = 8%, PV = 20,687.90

At IRR = 9%, PV = 19,925.35

Using Interpolation to find IRR

8% + (20,687.90- 20000)/(20,687.90 - 19925.35) x (9% - 8%)

8% + 0.90%

8.90%