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The formula for the present value (PV) of a future cash flow (CF_n) received in year n at an interest rate i is:

Accounting

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3 parts
i
16,124.28
ii
17,466.99
iii
14,942.39

Step-by-step solution

9 steps

Here's how to calculate the present value of the cash flow stream for each interest rate.

The formula for the present value (PVPV) of a future cash flow (CFnCF_n) received in year nn at an interest rate ii is:

PV=CFn(1+i)nPV = \frac{CF_n}{(1 + i)^n}

To find the total present value of a stream of cash flows, we sum the present values of each individual cash flow:

PVtotal=CF1(1+i)1+CF2(1+i)2+CF3(1+i)3PV_{total} = \frac{CF_1}{(1 + i)^1} + \frac{CF_2}{(1 + i)^2} + \frac{CF_3}{(1 + i)^3}

Given cash flows:
CF_1 = \5,000(attheendofyear1)(at the end of year 1) CF_2 = $6,000(attheendofyear2)(at the end of year 2) CF_3 = $8,000$ (at the end of year 3)

Part i· 3 steps

Interest rate = 8%

  1. Convert the interest rate to a decimal.

    i=8%=0.08i = 8\% = 0.08

  2. Calculate the present value of each cash flow.

    PV1=5,000(1+0.08)1=5,0001.08≈4,629.63PV_1 = \frac{5,000}{(1 + 0.08)^1} = \frac{5,000}{1.08} \approx 4,629.63 PV2=6,000(1+0.08)2=6,0001.1664≈5,143.99PV_2 = \frac{6,000}{(1 + 0.08)^2} = \frac{6,000}{1.1664} \approx 5,143.99 PV3=8,000(1+0.08)3=8,0001.259712≈6,350.66PV_3 = \frac{8,000}{(1 + 0.08)^3} = \frac{8,000}{1.259712} \approx 6,350.66

  3. Sum the present values to find the total present value.

    PVtotal=4,629.63+5,143.99+6,350.66=16,124.28PV_{total} = 4,629.63 + 5,143.99 + 6,350.66 = \boxed{16,124.28}

Part ii17,466.99

Interest rate = 4%

  1. Convert the interest rate to a decimal.

    i=4%=0.04i = 4\% = 0.04

  2. Calculate the present value of each cash flow.

    PV1=5,000(1+0.04)1=5,0001.04≈4,807.69PV_1 = \frac{5,000}{(1 + 0.04)^1} = \frac{5,000}{1.04} \approx 4,807.69 PV2=6,000(1+0.04)2=6,0001.0816≈5,547.34PV_2 = \frac{6,000}{(1 + 0.04)^2} = \frac{6,000}{1.0816} \approx 5,547.34 PV3=8,000(1+0.04)3=8,0001.124864≈7,111.96PV_3 = \frac{8,000}{(1 + 0.04)^3} = \frac{8,000}{1.124864} \approx 7,111.96

  3. Sum the present values to find the total present value.

    PVtotal=4,807.69+5,547.34+7,111.96=17,466.99PV_{total} = 4,807.69 + 5,547.34 + 7,111.96 = \boxed{17,466.99}

Part iii14,942.39

Interest rate = 12%

  1. Convert the interest rate to a decimal.

    i=12%=0.12i = 12\% = 0.12

  2. Calculate the present value of each cash flow.

    PV1=5,000(1+0.12)1=5,0001.12≈4,464.29PV_1 = \frac{5,000}{(1 + 0.12)^1} = \frac{5,000}{1.12} \approx 4,464.29 PV2=6,000(1+0.12)2=6,0001.2544≈4,783.16PV_2 = \frac{6,000}{(1 + 0.12)^2} = \frac{6,000}{1.2544} \approx 4,783.16 PV3=8,000(1+0.12)3=8,0001.404928≈5,694.94PV_3 = \frac{8,000}{(1 + 0.12)^3} = \frac{8,000}{1.404928} \approx 5,694.94

  3. Sum the present values to find the total present value.

    PVtotal=4,464.29+4,783.16+5,694.94=14,942.39PV_{total} = 4,464.29 + 4,783.16 + 5,694.94 = \boxed{14,942.39}
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