Question

Initial cash outlay is $50,000. The required rate of return is 9%. The length of time of the project is 6 years. Each year the project is expected to provide $12,500 of free cash flow.

1a. Calculate NPV

1b. Calculate the (estimated) IRR

Hint: start with (I.C.O. / F.C.F)

The existing 10 year, 6% bonds are trading in the market at $900. The corporate tax rate is 32%

Estimated YTM formula:

YTM=Coupon+par value-market valueyearsmarket value+par value2

After-tax interest rate = YTM (1-T)

2a. Calculate the interest rate for the new bonds.

2b.What is the after-tax interest rate for the new bonds?

Total assets of the firm is $5,000,000. Outstanding stock is 50,000 shares. EBIT is $500,000.

Corporate debt is 50% and the debt interest rate is 5%. The corporate tax rate is 40%.

EPS = NI / outstanding shares; ROE = NI / common equity

3. Calculate EPS

calculate ROE

Answer 1

1a. Particular Year0 Year 1 to 6

1.Initial Outflow    -$50,000 0000

2.Cash Inflow $12,500

3.Pv factor@ 9% 4.486

4.Present Value of Cash inflow (3*2) $56,075

NPV ( 4 - 1 ) $ 6,075

1b. Let another rate 10% for IRR calculation

Particular Year0 Year 1 to 6

1.Initial Outflow    -$50,000 0000

2.Cash Inflow $12,500

3.Pv factor@ 10%     4.355

4.Present Value of Cash inflow (3*2) $54438

NPV ( 4 - 1 ) $ 4438

IRR calculatio = R1​ + NPV1​×(R2​−R1​) / (NPV1​−NPV2​)

R1 = 10%

R2 = 9%

NPV1 = Higher Net Present value

NPV2 = Lower Net Present value

IRR = 10% + ($6075)* (  10% - 9% ) / ($6075 -$4438) = 10% + $6075/$1637 = 10% + 3.71% = 13.71%

2a. Lets 6% Bond Face value is $1000 and interest earned on this is $1000*6% = $60

Interest rate for New Bond = $60/ &900 * 100 = 6.67%

2b. Interest rate after tax = 6.67% ( 1- 32% ) = 4.536%

3. Calculation of EPS and ROE

TOTAL Assets = $5000,000

Corporate Debt@50% = $5000,000 * 50% = $25,00,000

Interest on Debt@ 5% = $25,00,000 * 5% = $1,25,000

1.EBIT = $ 500,000

2.(less) Interest on debt = ($ 1,25,000)

3.EBT (1-2) = $ 3,75000

4.(less) Tax@40% = ($1,50,000)

5. EAT OR NI (3-4)    = $2,25000

6. Outstanding No. of Shares    = 50,000

7. EPS (5/6) = $ 4.5

9. Common Equity = $25,00,000

10. ROE ( 5/9 * 100 ) = 9%