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Determine the Payback Period, the Discounted Payback Period, and the Net Present Value for the following...

Determine the Payback Period, the Discounted Payback Period, and the Net Present Value for the following after-tax cash flow projections. Also tell me whether the IRR is greater or less then the RRR.

A. Year ATCF

0 $(60,000)

1 21,000

2 27,000

3 24,000

4 16,000

Assume a 16% required rate of return

Solutions

Expert Solution

Payback Period = 2.50 Years

Discounted Payback Period = 3.73 Years

Net Present Value = $ 2,381.29

IRR = 18.042%

Since the IRR is 18.042% and the required rate of return is 16%, the IRR is greater than the RRR.

Note:

Payback Period = ( Last Year with a Negative Cash Flow ) + [( Absolute Value of negative Cash Flow in that year)/ Total Cash Flow in the following year)]

= 2+(12000/24000)

= 2.5 Years

Year Investment Cash Inflow Net Cash Flow
0 -60,000.00 -    -60,000.00 (Investment + Cash Inflow)
1 -    21,000.00 -39,000.00 (Net Cash Flow + Cash Inflow)
2 -    27,000.00 -12,000.00 (Net Cash Flow + Cash Inflow)
3 -    24,000.00 12,000.00 (Net Cash Flow + Cash Inflow)
4 -    16,000.00 28,000.00 (Net Cash Flow + Cash Inflow)

Discounted Payback Period =

( Last Year with a Negative Cumulative Cash Flow ) + [( Absolute Value of negative Cumulative Cash Flow in that year)/ Total Present Cash Flow in the following year)]

= 3+(6,455.36922383040/8,836.65756608)

= 3.73 Years

Cash Flow Discounting Factor ( 16%) Present Value (Cash Flow * Discounting Factor) Cumulative Cash Flow (Present Value of Current Year+ Cumulative Cash Flow of Previous Year)
0 -60,000 1 -60,000.00 -60,000.00000000000
1 21,000 0.862068965517 18,103.448275862 -41,896.55172413790
2 27,000 0.743162901308 20,065.398335315 -21,831.15338882280
3 24,000 0.640657673541 15,375.784164992 -6,455.36922383040
4 16,000 0.552291097880 8,836.657566088 2,381.28834225719

Net Present Value = [21000*1/(1.16)^1+27000*1/(1.16)^2+24000*1/(1.16)^3+16000*1/(1.16)^4]-60000

= $ 2,381.29

Let the IRR be x.

Now , Present Value of Cash Outflows=Present Value of Cash Inflows

60000 = 21000/(1.0x) +27000/ (1.0x)^2 +24000/(1.0x)^3+ 16000/(1.0x)^4     

Or x= 18.042%

Hence the IRR is 18.042%

jeff jeffy answered 2 years ago
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