Urban Summer provides inner-city children with summer camping experiences. They

Question

Urban Summer provides inner-city children with summer camping experiences. They are in the process of replacing all of their tents. Outdoor Outfitters has given them proposals for two different types of tents. The first is made by Lifelong Adventures (LA) and has an expected life of six years. The second, made by Outdoor Experiences (OE), lasts five years. The projected costs of buying and using the two types of tents are shown below. Urban Summer's cost of capital is 10%. Based on the projected cash flows below, which of the two tents should Urban Summer buy?

Period LA         OE

0         800        775

1               65          0

2               65           75

3               65           75

4              65            75

5    65           75

6              65 --

Explanation / Answer

Since the lifetime of the tents are different, we should calculate the NPV of the costs associated and calculate the annuity equivalent to the NPV to estimate the equivalent annual costs associated with each of the tents.
Cost of capital is 10%

So NPV of costs of LA
= 800 + 65/(1+10%) + 65/(1+10%)^2 + 65/(1+10%)^3 + 65/(1+10%)^4 + 65/(1+10%)^5 + 65/(1+10%)^6
= 1083

So NPV of costs of LA
= 775 + 75/(1+10%)^2 + 75/(1+10%)^3 + 75/(1+10%)^4 + 75/(1+10%)^5
= 991

annuity installment = NPV*r/[(1-(1+r)^-n]

LA
6 year annuity equivalent to 1083 at 10%
=NPV*r/[(1-(1+r)^-n]
=1083*10%/[(1-(1+10%)^-6]
=248.66

OE
5 year annuity equivalent to 991 at 10%
=NPV*r/[(1-(1+r)^-n]
=991*10%/[(1-(1+10%)^-5]
=261.42

So equivalent annual cost of LA is less than OE. So urban summer should buy the LA tent.

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