You have a project with the following CFs and a discount rate of 9.5%:9 yr6.12 yr11 yr10 yr8 yr7 yгб уг5 yr4 yrЗ yг2 yr1 yrToday-10,0001,313 1,797 1,968 1,724 1,7521,802 2,263 1,859 1,900 1,486899548What is the payback period for this investment?а.What is the discounted payback period for this investment?b.

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Asked Oct 27, 2019

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You have a project with the following CFs and a discount rate of 9.5%:
9 yr
6.
12 yr
11 yr
10 yr
8 yr
7 yг
б уг
5 yr
4 yr
З yг
2 yr
1 yr
Today
-10,000
1,313 1,797 1,968 1,724 1,7521,802 2,263 1,859 1,900 1,486
899
548
What is the payback period for this investment?
а.
What is the discounted payback period for this investment?
b.
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You have a project with the following CFs and a discount rate of 9.5%: 9 yr 6. 12 yr 11 yr 10 yr 8 yr 7 yг б уг 5 yr 4 yr З yг 2 yr 1 yr Today -10,000 1,313 1,797 1,968 1,724 1,7521,802 2,263 1,859 1,900 1,486 899 548 What is the payback period for this investment? а. What is the discounted payback period for this investment? b.

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Step 1

Payback period is the time when the cumulative cash flow turns out to be zero. Discounted payback period is when cumulative discounted cash flows turns out to be zero.

Approach:

  • We will calculate the cumulative cash flows each year
  • We will calculate the discount factor corresponding to each year using the formula, D = (1 + r)-t where r is the discount rate = 9.5% and t is the year number
  • We will then calculate the cumulative discounted cash flows
Step 2

Please see the white board. The cells highlighted in yellow deserve your attention. Figures in parenthesis, if any, mean negative values.&nb...

Cumulative of
Discounted Cumulative
cash flows cash flows
Discount
discounted
Year
Cash flows
Factor
cash flows
Cumulative Cumulative of
(1+ r)t DCF = C x D
C
D
of C
DCF
(10,000.00) (10,000.00)
(9,452.00)
(8,553.00)
(7,240.00)
(5,443.00)
(10,000.00)
(10,000.00)
0
1.0000
548.00
(9,499.54)
0.9132
500.46
(8,749.77)
2
899.00
0.8340
749.78
(7,749.72)
1,313.00
0.7617
1,000.05
(6,499.77)
4
1,797.00
0.6956
1,249.95
(3,475.00)
(1,751.00)
(5,249.64)
(4,249.52)
(3,321.33)
(2,449.48)
5
1,968.00
0.6352
1,250.13
6
1,724.00
0.5801
1,000.12
7
1,752.00
0.5298
928.19
1.00
8
1,802.00
0.4838
871.85
1,803.00
999.90
(1,449.58)
2,263.00
0.4418
4,066.00
750.13
5,925.00
(699.45)
10
1,859.00
0.4035
1,900.00
11
0.3685
700.16
7,825.00
0.71
12.
1,486.00
0.3365
500.09
9,311.00
500.80
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Cumulative of Discounted Cumulative cash flows cash flows Discount discounted Year Cash flows Factor cash flows Cumulative Cumulative of (1+ r)t DCF = C x D C D of C DCF (10,000.00) (10,000.00) (9,452.00) (8,553.00) (7,240.00) (5,443.00) (10,000.00) (10,000.00) 0 1.0000 548.00 (9,499.54) 0.9132 500.46 (8,749.77) 2 899.00 0.8340 749.78 (7,749.72) 1,313.00 0.7617 1,000.05 (6,499.77) 4 1,797.00 0.6956 1,249.95 (3,475.00) (1,751.00) (5,249.64) (4,249.52) (3,321.33) (2,449.48) 5 1,968.00 0.6352 1,250.13 6 1,724.00 0.5801 1,000.12 7 1,752.00 0.5298 928.19 1.00 8 1,802.00 0.4838 871.85 1,803.00 999.90 (1,449.58) 2,263.00 0.4418 4,066.00 750.13 5,925.00 (699.45) 10 1,859.00 0.4035 1,900.00 11 0.3685 700.16 7,825.00 0.71 12. 1,486.00 0.3365 500.09 9,311.00 500.80

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