Payback Period, IRR, and Minimum Cash Flows The management of Mohawk Limited is
ID: 2572415 • Letter: P
Question
Payback Period, IRR, and Minimum Cash Flows The management of Mohawk Limited is currently evaluating the following investment proposal: Time 0 Year 1 Year 2 Year 3 Year 4 Initial investment Net operating cash inflows $150,000 50,000 $50,000 50,000 $50,000 (a) Determine the proposal's payback period. 3 years (b) Determine the proposal's internal rate of return. (Refer to Appendix 128 if you use the table approach.) 12.56 % (c) Given the amount of the initial investment, determine the minimum annual net cash inflows required to obtain an internal rate of return of 16 percent. Round the answer to the nearest dollar. $53,604X CheckExplanation / Answer
(a)
Year
Cash Flow
Cumulative cash flow
0
$ (150,000)
$ (150,000)
1
$ 50,000
$ (100,000)
2
$ 50,000
$ (50,000)
3
$ 50,000
$ (0)
4
$ 50,000
$ 50,000
Payback period = A + B/C
Where,
A = last period with a negative cumulative cash flow = 2 years
B = absolute value of cumulative cash flow at the end of the period A = $ 50,000
C = total cash flow during the period after A = $ 50,000
Payback period = 2 + $ 50,000/$ 50,000 = 2 + 1 = 3 years
(b)
Let us use trial and error method for computation of IRR.
Let us try with 12 %
Year
Cash Flow
PV Factor Formula
PV Factor @ 12 %
PV
0
$ (150,000)
1/(1+0.12)^0
1.00000
$ (150,000.00)
1
$ 50,000
1/(1+0.12)^1
0.89286
$ 44,642.86
2
$ 50,000
1/(1+0.12)^2
0.79719
$ 39,859.69
3
$ 50,000
1/(1+0.12)^3
0.71178
$ 35,589.01
4
$ 50,000
1/(1+0.12)^4
0.63552
$ 31,775.90
NPV1
$ 1,867.47
As NPV is positive let us try with 13 %
Year
Cash Flow
PV Factor Formula
PV Factor @ 13 %
PV
0
$ (150,000)
1/(1+0.13)^0
1.00000
$ (150,000.00)
1
$ 50,000
1/(1+0.13)^1
0.88496
$ 44,247.79
2
$ 50,000
1/(1+0.13)^2
0.78315
$ 39,157.33
3
$ 50,000
1/(1+0.13)^3
0.69305
$ 34,652.51
4
$ 50,000
1/(1+0.13)^4
0.61332
$ 30,665.94
NPV2
$ (1,276.43)
IRR = R1 +NPV 1 (R2-R1)% / (NPV1-NPV2)
=12% + $ 1,867.47 (13-12)% /($ 1,867.43 -(-$1,276.43)
=12% + $ 1,867.47 x 1 % /$ 1,867.43 + $ 1,276.43
=12% +$ 18.6747 / $ 3,143.90
= 12 % + 0.005939969
= 12 % + 0.59 %
= 12.59 %
(c)
At discout rate of IRR, NPV = 0.
Let the even cash flows for 1st to 4th years be C.
Putting cash flows as C and NPV as 0, we get C as:
0 = C/(1+0.16) + C/(1+0.16)2+ C/(1+0.16)3+ C/(1+0.16)4 - $ 150,000
$ 150,000 = C/(1.16) + C/(1.16)2+ C/(1.16)3+ C/(1.16)4
$ 150,000 = C /1.16 + C /1.3456 + C/1.560896 x + C/1.81063936
$ 150,000 = C x 0.862068966 + C x 0.743162901 + C x 0.640657674 + C x 0.552291098
$ 150,000 = C x (0.862068966 + 0.743162901 + 0.640657674 + 0.552291098)
$ 150,000 = C x 2.798180638
C = $ 150,000/2.798180638 = $ 53,606.260 or $ 53,606
Year
Cash Flow
Cumulative cash flow
0
$ (150,000)
$ (150,000)
1
$ 50,000
$ (100,000)
2
$ 50,000
$ (50,000)
3
$ 50,000
$ (0)
4
$ 50,000
$ 50,000
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.