Question

A company is planning to build an engineering lab at a nearby university through a grant. The building should initially cost $50,000,000 and maintenance cost(end of year) are expected to be $200,000 per year for the first 3 years, $300,000 per year for the next 4 years, and then $400,000 per year after. If the grant will be invested at 10%, how large a donation must the company make? (assume the term is unlimited and lab lasts forever)

Answer 1

This is an example of three stage model. In the first stage the maintenance is $200,000 for the first three years. Then again $300,000 for the next 4 years and eventually $400,000 forever.

For 400,000 first we need to find the horizon cost by dividing constant cash flow of $400,000 by the rate and then dicounting it to the present value.

Horizon cost is done as follows : 400000 / r = 400000 / 0.10 = 4000,000

The present value of these outflows is calculated as follows

PV = 50,000,000 + 200,000 / (1+r) + 200,000 / (1+r)^2 + 200,000 / (1+r)^3 + 300,000 / (1+r)^4 + 300,000 / (1+r)^5 + 300,000 / (1+r)^6 + 300,000 / (1+r)^7 + Horizon cost / ( 1+ r)^7

PV = 50,000,000 + 200,000 / (1+0.10) + 200,000 / (1+0.10)^2 + 200,000 / (1+0.10)^3 + 300,000 / (1+0.10)^4 + 300,000 / (1+0.10)^5 + 300,000 / (1+0.10)^6 + 300,000 / (1+0.10)^7 + 4000000 / ( 1+ 0.10)^7

PV = 50,000,000 + 181818.18 + 165289.3 + 150263 + 204904 + 186276.4 + 169342.2 + 153947.4 + 2052632.5

PV = $53264472.9

The company should make a donation of $53,264,472.9