Question

1. Developed Investments Enterprises (DIE) is trying to secure a $5,000,000 loan to develop a piece of property in downtown Amherst. Several banks have offered financing for the project. The options are:
   1. A 10-year loan with annual payments of $660,000.
   2. A 10-year interest only loan at 5% per year.
   3. A 10-year discount loan with a single payment of $8,790,000 being due after 10 years.

Which loan should DIE’s CFO accept and why?

2. State of Massachusetts has a new lottery. The winner will have the option of picking among these prizes. If deposit and loan rates at local banks are 4.5% per year, which prize should you select and why? Which one is better and why?

1. $1,000,000 Cash today.
2. $46,000 a year forever starting a year from now.
3. $26,000 a year forever starting a year from now with payments growing at the rate of inflation, which is expected to be 2% per year.
4. $125,000 a year for 10 years starting a year from now.

Answer 1

1).

Option a: A 10-year loan with annual payments of $660,000

This will have a total payment of 660,000*10 = 6,600,000

Option b: A 10-year interest only loan at 5% per year

This will have an interest payment of 5%*5,000,000 = 250,000 per annum

So, total payment = 250,000*10 + principal = 2,500,000 + 5,000,000 = 7,500,000

Option c: A 10-year discount loan with a single payment of $8,790,000 being due after 10 years

This will have a total payment of 8,790,000

Out of all the 3 options, option a has the lowest total payment so that should be chosen.

2). Present Value (PV) of option a is 1,000,000 today.

PV of option b is 46,000/4.5% = 1,022,222.22

PV of option c is 26,000/(4.5%-2%) = 1,040,000

PV of option d is: PMT = 125,000; N = 10; rate = 4.5%, solve for PV. PV = 989,089.77

Choose option c as it has the maximum payout.