Question

1. a) What is the net present value of a project that has upfront costs of $5 million and pays end of the year cash flows of $1 million in one year, $2 million in two years, and $3 million in three years if the annual discount rate for the project is 3 percent? Show how much money you would have at the end of three years if you bought the project and what you would have instead if you banked your $5 million for three years at 3 percent.

b) Your agency is competing with another agency for $15 million in government money. Only one of you will get the $15 million. Your agency will use the $15 million for vocational training that will increase the skills and earning power of 100 people in about two years when they finish the program. The other agency will use the $15 million to study how floods affect homeowners’ insurance costs. Their study will take four years but it will create twice as much value as your agency’s project at the end of that time. The government uses a 4 percent discount rate for both projects. Who will get the $15 million?

c) Calculate the Net Present Value of a project that has upfront costs of $124,000 and end-of-year annual cash flows of $30,000 for five years, if the appropriate discount rate is 6.5 percent. Suppose that discount rate is the borrowing cost for the project. Show that this project’s cash flows can pay off a loan with an annual interest rate of 6.5 percent over the next five years.

Answer 1

Answer: A Present value formula = Net cash flow /(1+ discount rate)^(no of years)

Figures in Millions
Year	0	1	2	3
Upfront cost	-5
Cash Flows		1	2	3
Present value	-5	0.970874	1.885192	2.745425
NPV	0.601491

If we bought the project, lets assume the net cash flow that we will get in year 1 and 2, we  will invest and get 3% return on that amount

Future value = present value * ( 1 + interest rate) ^(no of years)

for year 1 cash flow = 1* (1+0.03)^2

For year 2 cash flow 2*(1+0.03)^1

Year	1	2	3
Cash Flows	1	2	3
Future value at the end of 3 year of yearly cash flow	1.06	2.06	3
Total Future Value of cash flow at the end of 3rd year	6.12
On banking the same amount future value	5.46	5*(1+0.03)^3

Purchasing the project is better for us

B.) Lets say training project creates a value of 100 million at the end of 2nd year

then flood study will create a value of 200 million at the end of 4th year

Discounting both at 4 % lets see who has created the better value

Present value of training project = 100/(1+0.04)^2 = 92.45

Present value of Research project = 200/(1+0.04)^4 = 170.9

As present value is higher in the Research project this will get the government money of $15 million

C) Calculate the present value of all the future cash flow by doing this project if it exceeds the $124000 amount that means we can do this project

Year	0	1	2	3	4	5
Upfornt cost	-124000
Cash Flow		30000	30000	30000	30000	30000
Present value		28,169	26,450	24,835	23,320	21,896
NPV		124,670

As NPV is higher than 124000 we are sure that this project is beneficial for us

Value of 124000 at the rate of 6.5%

Future value = 124000*(1+0.065)^5 = 169890.7

Assume that the project cash flows are reinvested at 6.5% only

Year	0	1	2	3	4	5
Cash Flow		30000	30000	30000	30000	30000
Future value at the end of 5th year		38593.99	36238.49	34026.75	31950	30000
Total Future value at the end of 5th year		170,809

This value is higher than 169890.7 which shows that we can repay the loan through this