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Both types of payback period, 3000 investment

Short answer

Simple payback is 3.08 years; discounted payback at 10% MARR is 3.75 years. The discounted period is longer because of the time value of money.

From the following cash flow, calculate both types of payback period. MARR = 10%.

EOY012345
Cash flow-30008001000110012101464
 EOY : 0      1    2     3     4     5
 CF  : -3000  800  1000  1100  1210  1464
EOYCFCumulative CFPW at 10%Cumulative PW
0-3,000-3,000-3,000.00-3,000.00
1800-2,200727.27-2,272.73
21,000-1,200826.45-1,446.28
31,100-100826.45-619.83
41,2101,110826.45206.61
51,4642,574909.031,115.64

Simple payback

Cumulative CF is −100 at year 3 and +1,110 at year 4.

θ = 3 + 100 / 1,210 = 3.08 years

Discounted payback (MARR = 10%)

Cumulative PW is −619.83 at year 3 and +206.61 at year 4.

θ_d = 3 + 619.83 / 826.45 = 3.75 years

Answer: simple payback = 3.08 years; discounted payback = 3.75 years. The discounted period is longer because future inflows are worth less today. If the firm's cut-off is more than 3.75 years, the project is accepted by both.

✓ Answer checked by Claude Opus 5.5 (high effort)

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