I have this homework assignment that I don't fully understand. I think I'm close to the solution but I'm not 100% sure.
A person is able to obtain a loan (subsidary) from the government if he makes an investment in a specific project. The interest rate of the loan is 2% p.a., it's 10 years and it's a loan where pay only interests each year (I don't know what that's called in english :)). So let's say he borrows $1,000,000. Each year he pays $20,000 and after 50 years he pays $1,000,000. The project gives him a normal profit, let's say 6% p.a. I now have to determine the value of this subsidary. My interpretation of this question is, that I have to calculate the NPV of the subsidary. Clearly the value is in the difference between the interest rates. So I think the solution is something like this:
NPV = (.06-.02)*1,000,000A(10,6%) = 294,403
I'm not sure about 2 things:
1) If I invest 1,000,000 in the project I will get $60,000 in interest the first year and I have to pay $20,000 (loan interest). Year 2 I get $60,000+0.06*$60,000 from the investment but I still only have to pay $20,000. Above I assume that my net cash flow each year is $40,000 right? This is not true, is it?2) What discount rate should I use? Above I'm using 6%, but I don't quite understand how to determine an appropriate discount rate. And why exactly should I discount the net profit ($40,000) back to year 0? My books says that the discount rate is the risk free rate + inflation
- risk or that it can be considered as an opportunity cost. Does this mean that if I had .000 in year 1 (earned from the investment minus loan) then this amount is worth 37,736 today if I had invested them elsewhere to 6%? What I don't understand is, that he already invested them in the mention project, so why discount the amount back again with the same interest rate?
I really hope that someone is able to clarify this for me :)