An investor agreed to sell a warehouse five years from now to the tenant who currently rents the space. The tenant will continue to pay $20,000 rent at the end of each year including year 5 in which he will purchase the building for an additional $150,000. Assuming the investor's required rate of return is 10%, how much is this deal presently worth to the investor who was willing to sell?

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TomShelby TomShelby · Answer 1 · 2019-08-10T20:27:00+02:00

Answer:

Net present value of $168,953.93

Explanation:

We will calculate the present value of the cash flow at the investor's rate of return.

First we have the annuity of 20,000 during 5 years

[tex]C \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]

C = 20,000

time = 5

rate = 10

[tex]20,000 \times \frac{1-(1+0.10)^{-5} }{0.10} = PV\\[/tex]

PV = 75,815.73539

Then we calculate the present value of the final payment of 150,000

[tex]\frac{Nominal}{(1 + rate)^{time} } = PV[/tex]

Nominal = 150,000

rate = 0.1

time = 5

[tex]\frac{150,000}{(1 + 0.10)^{5} } = PV[/tex]

PV = 93,138.198459

We add both together: And get the present value

75,815.73 + 93,138.20 = 168,953.93