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EX1:

A machine costs $380,000 and is expected to produce the following cash flows:

Year	1	2	3	4	5	6	7	8	9	10
Cash flow (thousand dollars)	50	57	75	80	85	92	92	80	68	50

The cost of capital is 12%, what is the machine’s NPV?

EX2:

What is the future value of the following cash flow at the end of five years with the discount rate of 10%?

Year	0	1	2	3	4	5
Cash flow	$23,000	$55,000	0	-$15,000	$18,000	$33,000

EX3:

The interest rate is 10%.

a) What is the PV of an asset that pays $1 a year in perpetuity?

b) A piece of land produces an income that grows by 5% per annum. If the first year’s income is $10,000, what is the value of the land?

EX4:

What is the present value of a project that generates cash flows of $4,325 starting from the end of year 4 in perpetuity. In two cases:

a) Assuming that the required return is 13%.

b) Assuming that the required return is 13% and a constant growth rate of the cash flows is 4%.

EX5:

Lan receives 3.2 million VND on the first day of each month while Mai receives 3.2 million VND on the last day of each month. Both Lan and Mai will receive the payments for 4 years. The discount rate is 6.5 percent, compounded monthly. What is the difference in the present value of these two sets of payments?

EX6: You plan to buy a Jaguar XJ for $28,000, but you have only $6,000 in cash. The bank will loan you the rest at the annual interest rate of 12%, with the payments spread over 60 months. Find your monthly payment.

EX7: You can deposit $4000 per year into an account that pays 12% interest. If you deposit such amounts for 15 years and start drawing money out of the account in equal annual installments, how much could you draw out each year for 20 years?