# Yield in presence of bank finance

A project is to build a windmill. It will cost $$£1,000,000$$ to build and it will generate income (after costs) of $$£80,000$$ per year, paid annually for fifty years, with the first payment made in 2 years’ time. Bank finance is available at the rate of 6% (annual effective rate). Show that the yield is approximately $$7.2\%$$.

What should this bank finance mean? If we ignored it (as the question has a lot of parts, so I thought I might not need it now), we would consider

$$0 = -1000000 + 80000\sum_{k=2}^{51}v^k = -10^6 + 8\times 10^4 \times \frac{v^{52}-v^2}{v-1}$$

But in this case $$i = 7.2%$$ (i.e. $$v \sim 0.993$$ is quite far from the solution of the above equation.

Any help appreciated!

• You have cash inflows of 80,000 per year, and you also have out flows to services the debt. You can't ignore paying back the construction loan. – saulspatz May 29 at 1:52
• Sorry, could you give more detail? – DesmondMiles May 29 at 8:41
• Actually, I was wrong. They are ignoring the bank financing. I get $$80000\sum_{n=2}^{50}(1.072)^{-n}\approx1,002,127.01$$ I don't understand what this yield is supposed to represent, though. – saulspatz May 29 at 13:36
• I would post this at quant.stackexchange.com instead. – Rodrigo de Azevedo Jun 1 at 12:21