Question file attached.
Question 2 asks about your friend that now would demand 30% return instead of the 20% that was originally part of your loan. Since you are receiving 20% on the loan, at the end of the year your friend would give you $120 (100 principal + 20 interest). Since your friend demands a 30% rate of return the price he/she would pay would be 120/1.3
Most of the other questions follow in that format, you will be discounting back to the present value using a required rate of return.
In # 3, you will be doing essentially the same thing, although a little more complicated.
You start out with 60 million cash from day one. You expect to earn 5,000,000 in the first year with a required rate of return, so you would divide the 5 million by 1.12 to get the present day value of what you would pay for those returns in the future. Since the business would grow by 30% over the next 2 years, in year 2 your earnings would be 5 million time 1.3, and in year 3 your earnings would be 5 million times 1.3 squared.
The mathematical equation would end up looking like below:
60,000,000+ (5,000,000/1.12) + ((5,000,000*1.3)/(1.12)^2) + ((5,000,000*1.3*1.3)/(1.12)^3)
1. As quoted from this site http://www.brydels.com/chapter10.html the historical return of a long term bond is around 5.8%, with a standard deviation of 9.3%. We will round the numbers slightly and say that the long term bond return is 6% and 10% standard deviation. You would only have to purchase long term bonds in this case. (Generally speaking, 6% annual return is a fairly low target. Look at here http://pages.stern.nyu.edu/~adamodar/New_Home_Page/datafile/histret.html, some years bonds can achieve a 25% return a year!)
To see when you will lose money, we assume that the return is ...
Securities and Portfolios: Asset allocation; risk free rate, value of equity, sales growth