Cannonier, Inc., has identified an investment project with the following cash fl
ID: 2612547 • Letter: C
Question
Cannonier, Inc., has identified an investment project with the following cash flows.
Year Cash Flow
1 $ 1,020
2 1,250
3 1,470
4 2,210
If the discount rate is 6 percent, what is the future value of these cash flows in Year 4? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
Future value $
What is the future value at a discount rate of 14 percent? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
Future value $
What is the future value at a discount rate of 21 percent? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
Future value $
Explanation / Answer
Answer: The discounted cash flow for the year 'N' is:-
Discounted Cash Flow for the year 'N' = DCFN = Cash Flow for the year 'N' / (1 + r)^'N', where r is the discount rate - see link below.
If we take the first discount rate you mention: r = 6%, the discounted cash flow for the four years are:-
DCF1 = $1,020 /(1+6%)^1 = $1020/1.0600 = $962.264
DCF2 = $1,250 /(1+6%)^2 = $1,250/1.1236 = $1,112.50
DCF3 = $1,470 /(1+6%)^3 = $1,470/1.191016 = $1,234.24
DCF4 = $2210 /(1+6%)^4 = $2210/1.2625 = $1750.50
Add up the 4 figures, to get the future value of the cash flows in year 4: $962.264 + $1,112.50 + $1,234.24 + $1,750.50 = $5,059.504.
If we take the first discount rate you mention: r = 14%, the discounted cash flow for the four years are:-
DCF1 = $1,020 /(1+14%)^1 = $1020/1.14 = $894.74
DCF2 = $1,250 /(1+14%)^2 = $1,250/1.2996 = $961.8344
DCF3 = $1,470 /(1+14%)^3 = $1,470/1.481544 = $992.208
DCF4 = $2210 /(1+14%)^4 = $2210/1.68896 = $1308.4975
Add up the 4 figures, to get the future value of the cash flows in year 4: $894.74 + $961.8344 + $992.208 + $1,308.4975 = $4157.28.
If we take the first discount rate you mention: r = 21%, the discounted cash flow for the four years are:-
DCF1 = $1,020 /(1+21%)^1 = $1020/1.21 = $842.98
DCF2 = $1,250 /(1+21%)^2 = $1,250/1.4641 = $853.77
DCF3 = $1,470 /(1+21%)^3 = $1,470/1.771561 = $829.78
DCF4 = $2210 /(1+21%)^4 = $2210/2.1436=$1030.98
Add up the 4 figures, to get the future value of the cash flows in year 4: $842.98 + $853.77 + $829.78 + $1,030.98 = $3557.51.
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