Question

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?

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.

Would you suggest your firm invest in a new machine that costs $450,000 and generates cash flows of $60,000 per year at the end of each of the next ten years if the appropriate discount rate for the machine is 8 percent? What is the present value of the annuity generated by this machine’s cash flows?

Calculate the internal rate of return for a project that has upfront costs of $6 million and cash flows of $2 million per year for each of the next four years. Suppose the risk adjusted borrowing cost of this project is 15 per-cent. Using IRR analysis, would you undertake this project? Confirm your answer by calculating the project’s NPV.

Answer 1

PART-1

Let's Assume Future Value be "X" for vocational training. Therefore, future value for study on how flood affects insurance cost for homeowners be "2X"

Future Value = Present Value *(1+r)^n

FV = PV (1+r)^n where, "r" represents discount rate and "n" represents period

Now, calculate Future Value for Vocational Training Programme

FV = $15000000*(1+.04)^2

FV = $15000000*1.0816 = $16224000

Based on above-derived value, the future value of the second project "study on how flood affects insurance cost for homeowners" be $32448000. Using this future value, we shall calculate PV for the second project

FV = PV (1+r)^n

PV = FV/(1+r)^n

PV = $32448000/(1.04)^4

PV = $32448000/ 1.1699

PV = $27735703.91

Since PV of the second project is higher than the initial funding of 15 million, it is advisable to fund the second project.

Part-2

Upfront Cost $ 124000

Annual Cash Flow $ 30000

Discount Rate 6.5%

Period 5 years

Period	Inflow	Outflow	Net Inflow	Future Value
1	$30000	$8060*	$21940	$21940*(1+.065)^4 =$28225.07
2	$30000	$8060	$21940	$21940*(1+.065)^3 =$26502.41
3	$30000	$8060	$21940	$21940*(1+.065)^2 =$24884.90
4	$30000	$8060	$21940	$21940*(1+.065)^1 =$23366.10
5	$30000	$8060	$21940	$21940
Future Value After 5 Years				$124918.48

* (124000 * 6.5% = 8060, being yearly interest)

Since Future Value after 5 years is higher than the loan amount, hence, project can pay off the loan.

Part-3

Cost of New Machine $450000

Annual Cash Inflow $60000 for 10 years

Discount Rate is 8 %

Year	Cash Inflow	PVF @ 8%	Present Value
1	$ 60,000.00	1.0800	$      55,555.56
2	$ 60,000.00	1.1664	$      51,440.33
3	$ 60,000.00	1.2597	$      47,629.93
4	$ 60,000.00	1.3605	$      44,101.79
5	$ 60,000.00	1.4693	$      40,834.99
6	$ 60,000.00	1.5869	$      37,810.18
7	$ 60,000.00	1.7138	$      35,009.42
8	$ 60,000.00	1.8509	$      32,416.13
9	$ 60,000.00	1.9990	$      30,014.94
10	$ 60,000.00	2.1589	$      27,791.61
Present Value of Annuity			$   4,02,604.88

Part-4

Upfront Cost $ 6000000

Cash Inflow $ 2000000

Year	Cash Inflow	PVF @ 15%	Present Value
1	$ 20,00,000.00	1.1500	$17,39,130.43
2	$ 20,00,000.00	1.3225	$15,12,287.33
3	$ 20,00,000.00	1.5209	$13,15,032.46
4	$ 20,00,000.00	1.7490	$11,43,506.49
Present Value of future cash inflow			$57,09,956.73

Since, Present value of future cash inflow at 15% IRR is less than the amount invested. I would not undertake this project.