Question

Present and future values for multiple cash flows. Annuities and Perpetuities.

1. Buena Vista Co. has identified an investment project with the following cash flows. If the discount rate is 10%, what is the value of these cash flows today? What is the value today at 18%? At 24%?
Year Cash Flow
1 $720
2 930
3 1,190
4 1,275

Answer 1

To calculate the present value of the cash flows, discount them based on the given discount rate. The value at 10% discount rate is $3,199.74, at 18% is $2,333.53, and at 24% is $1,883.32.

Step-by-step explanation:

To calculate the present value of the cash flows, we need to discount them based on the given discount rate. Here are the calculations:

Discount rate: 10%

Year 1: $720 / (1 + 0.10) = $654.55

Year 2: $930 / (1 + 0.10)² = $751.31

Year 3: $1,190 / (1 + 0.10)³ = $901.02

Year 4: $1,275 / (1 + 0.10)⁴ = $892.86

Total value at 10% discount rate: $654.55 + $751.31 + $901.02 + $892.86 = $3,199.74

Discount rate: 18%

Year 1: $720 / (1 + 0.18) = $610.17

Year 2: $930 / (1 + 0.18)² = $600.92

Year 3: $1,190 / (1 + 0.18)³ = $572.33

Year 4: $1,275 / (1 + 0.18)⁴ = $550.11

Total value at 18% discount rate: $610.17 + $600.92 + $572.33 + $550.11 = $2,333.53

Discount rate: 24%

Year 1: $720 / (1 + 0.24) = $580.65

Year 2: $930 / (1 + 0.24)² = $500.54

Year 3: $1,190 / (1 + 0.24)³ = $431.62

Year 4: $1,275 / (1 + 0.24)⁴ = $370.51

Total value at 24% discount rate: $580.65 + $500.54 + $431.62 + $370.51 = $1,883.32