1.Write down the equation defining a projects internal rate of return (IRR). In practice

how is IRR calculated?

Without a computer or financial calculator, IRR can only be computed by trial and error

2.You have the chance to participate in a project that produces the following cash flows:

Cash Flows ($) C0 C1 C2

5,000 4,000 -11,000

The internal rate of return is 14 percent. If the opportunity cost of capital is 10 percent,

would you accept the offer?

3.Calculate WACC.

Source of capital	Cost	Sum
Loan 1	12%	14000
Loan 2	15%	6000
Equity		20000

Estimate the cost of equity through CAPM. Companys beta is 1.2, market portfolio rate of return is 15%, risk-free rate of return is 7%.

4.What is sensitivity analysis?

5. A company ? is planning to issue bonds with Face Value of 1000 rubles and annual coupon rate of 11%. Bonds will mature in 7 years, coupons are paid annually. The number of outstanding bonds is 1000 000. Profit tax rate is 20%. What is the cost of this source of capital?

6.Construct after-tax cash flows. Working capital is estimated as 15% of sales.

	1	2	3	4	5
Revenues	3000000	3 600000	4200000	4500000	5000000
Operating Expenses
Salaries	300000	330000	360000	390000	400000
Raw Material	1500000	1900000	2200000	2500000	2800000
Depreciation	200000	200000	200000	200000	200000
Operating Income
Taxes (20%)
Operating Income After Taxes
	0	1	2	3	4	5
Capital Expenditure	-10000000
After tax operating Income
Depreciation
Change in Working Capital
After-tax Cash Flows

7.You win a lottery with a prize of $1.5 million. Unfortunately the prize is paid in 10 annual

installments. The first payment is next year. How much is the prize really worth?

The discount rate is 8 percent.

1. a. Calculate (write down a formula) the net present value of the following project for discount rates of 0, 50, and 100 percent:

Cash Flows ($) C0 C1 C2

6,750 4,500 18,000

2. What is the IRR of the project (write down a formula)?

3.Suppose you have the following investment opportunities, but only $90,000 available

for investment. Which projects should you take?

Project NPV Investment

1 5,000 10,000

2 5,000 5,000

3 10,000 90,000

4 15,000 60,000

5 15,000 75,000

6 3,000 15,000

4.Calculate WACC.

Source of capital	Cost	Sum
Loan 1	12%	14000
Loan 2	15%	6000
Equity		20000

Estimate the cost of equity through CAPM. Companys beta is 1.2, market portfolio rate of return is 15%, risk-free rate of return is 7%.

5.What is VaR? How it can be calculated?

6.Construct after-tax cash flows.Working capital is estimated as 20% of sales.

		1	2	3	4	5
Revenues		3000000	3 600000	4200000	4500000	5000000
Operating Expenses
Salaries		300000	330000	360000	390000	400000
Raw Material		1500000	1900000	2200000	2500000	2800000
Depreciation		200000	200000	200000	200000	200000
Operating Income
Taxes (20%)
Operating Income After Taxes
		0	1	2	3	4	5
Capital Expenditure		-10000000
After tax operating Income
Depreciation
Change in Working Capital
After-tax Cash Flows

7. A piece of land produces an income that grows by 5 percent per annum. If the first

years flow is $10,000, what is the value of the land? The interest rate is 10 percent.

1.Write down the equation defining a projects internal rate of return (IRR). In practice

how is IRR calculated?

2.You have the chance to participate in a project that produces the following cash flows:

Cash Flows ($) C0 C1 C2

8,000 5,000 -14,000

The internal rate of return is 5 percent. If the opportunity cost of capital is 10 percent,

would you accept the offer?

3.Calculate WACC.

Source of capital	Cost	Sum
Loan 1	14%	15000
Loan 2	16%	5000
Equity		30000

Estimate the cost of equity through CAPM. Companys beta is 1.3, market portfolio rate of return is 17%, risk-free rate of return is 6%.

4.What is sensitivity analysis?

5. A company ? is planning to issue bonds with Face Value of 1000 rubles and annual coupon rate of 8%. Bonds will mature in 5 years, coupons are paid annually. The number of outstanding bonds is 1000 000. Profit tax rate is 20%. What is the cost of this source of capital?

6.Construct after-tax cash flows. Working capital is estimated as 25% of sales.

	1	2	3	4	5
Revenues	3000	3 600	4200	4500	5000
Operating Expenses
Salaries	300	330	360	390	400
Raw Material	1500	1900	2200	2500	2800
Depreciation	400	400	400	400	400
Operating Income
Taxes (20%)
Operating Income After Taxes
	0	1	2	3	4	5
Capital Expenditure	-10000
After tax operating Income
Depreciation
Change in Working Capital
After-tax Cash Flows

7. Harold Filbert is 30 years of age and his salary next year will be $20,000. Harold forecasts

that his salary will increase at a steady rate of 5 percent per annum until his retirement at age 60.

a. If the discount rate is 8 percent, what is the PV of these future salary payments?

b. If Harold saves 5 percent of his salary each year and invests these savings at an

interest rate of 8 percent, how much will he have saved by age 60?

1. a. Calculate (write down a formula) the net present value of the following project for discount rates of 0, 30, and 100 percent:

Cash Flows ($) C0 C1 C2

6,750 4,500 18,000

2. What is the IRR of the project (write down a formula)?

3.Suppose you have the following investment opportunities, but only $120,000 available

for investment. Which projects should you take?

Project NPV Investment

1 5,000 30,000

2 5,000 5,000

3 10,000 100,000

4 15,000 40,000

5 15,000 55,000

6 3,000 25,000

4.Calculate WACC.

Source of capital	Cost	Sum
Loan 1	14%	4000
Loan 2	16%	6000
Equity		10000

Estimate the cost of equity through CAPM. Companys beta is 1.1, market portfolio rate of return is 20%, risk-free rate of return is 8%.

5.What is VaR? How it can be calculated?

6.Construct after-tax cash flows.Working capital is estimated as 30% of sales.

		1	2	3	4	5
Revenues		3000000	3600000	4200000	4500000	5000000
Operating Expenses
Salaries		300000	330000	360000	390000	400000
Raw Material		1700000	2000000	2400000	2500000	3000000
Depreciation		200000	200000	200000	200000	200000
Operating Income
Taxes (20%)
Operating Income After Taxes
		0	1	2	3	4	5
Capital Expenditure		-10000000
After tax operating Income
Depreciation
Change in Working Capital
After-tax Cash Flows

7. Harold Filbert is 30 years of age and his salary next year will be $20,000. Harold forecasts

that his salary will increase at a steady rate of 5 percent per annum until his retirement at age 60.

a. If the discount rate is 8 percent, what is the PV of these future salary payments?

b. If Harold plans to spend these savings in even amounts over the subsequent 20 years, how much can he spend each year?

A piece of land produces an income that grows by 5 percent per annum. If the first

years flow is $10,000, what is the value of the land? The interest rate is 10 percent.

Harold Filbert is 30 years of age and his salary next year will be $20,000. Harold forecasts

that his salary will increase at a steady rate of 5 percent per annum until his retirement

at age 60.

a. If the discount rate is 8 percent, what is the PV of these future salary payments?

b. If Harold saves 5 percent of his salary each year and invests these savings at an

interest rate of 8 percent, how much will he have saved by age 60?

c. If Harold plans to spend these savings in even amounts over the subsequent 20

years, how much can he spend each year?