Question

Raymond Mining Corporation has 8.5 million shares of common stock outstanding and 135,000 quarterly bonds outstanding with face value $1000 and coupon rate of 7.5%. The common stock currently sells for $34 per share and has a beta of 1.25, and the bonds have 15 years to maturity and sell for 114 percent of the face value. The market risk premium is 7.5 percent, T-bills are yielding 4 percent (thus risk free rate is 4%), and Raymond Mining tax rate is 35%. Raymond Mining is considering an investment which will cost $2,590,000. The investment produces no cash flows for the first year. In the second year, the cash inflow is $580,000. This inflow will increase to $1,500,000 and then $2,000,000 for the following years before ceasing permanently (thus the project has in total 4 years).

1.What is the Internal Rate of Return for the above project?

2.Assuming that in the previous calculation you would find WACC to be 10% and IRR to be 20%, would you accept this project?

3.Assuming a WACC of 10%, what is the Discounted Payback Period for this project?

4.Assuming a WACC of 10%, what is the Profitability Index for this project?

Answer 1

First, we calculate the YTM of the quarterly bond using a financial calculator

PV = -1140

FV=1000

N=60 (Since 15 years = 60 quarterly payments)

PMT = 18.75 ( Since 7.5% annual coupon quarterly equals 7.5%*1000/4)

We get I/Y = 1.514

We annualise the YTM

YTM = 1.514*4 = 6.07%

Required rate of return R(e) using CAPM

R(e) = R(f) + Beta*(Market risk premium)

R(e) = 0.04+1.25*0.075 = 0.13375

R(e) = 13.375%

To calculate weight of debt and equity for WACC calculation

Value of equity = Total shares outstanding*stock value

Value of equity =8,500,000*34 = 289000000

Value of debt = No of bonds*Current price of the bond

Value of debt = 135000*1140 = 153900000

Total value = Value of equity+Value of debt = 289000000 + 153900000 = 442900000

Now WACC = Weight of equity*cost of equity + Weight of debt*After-taxcost of debt

WACC = (289000000/442900000)*13.375 + (153900000/442900000)*6.07*(1-0.35)

WACC= 10.09%

1) The IRR can be calculated on a calculator by entering the cash flows or on excel

Hence, the IRR = 14.71%

2)

Since the IRR is greater than WACC, we should accept this project

3)

WACC	10.01%
Year	Cash-flows	PV of the cash-flow (Cash-flow/((1+WACC)^Year)	Cumulative PV cash-flows
0	-2590000	-2590000	-2590000
1	0	0	-2590000
2	580000	479251.7023	-2110748.298
3	1500000	1126664.901	-984083.3965
4	2000000	1365530.287	381446.8901
IRR	14.71%
IRR Formula	IRR(B4:B8)

The discounted payback period is the time period at which NPV is 0

We observe that the cumulative PV cash-flow become 0 somewhere between year 3 and 4

Hence, the discounted pay-back = 3 years + (984083.39/1365530.28) = 3.72 years

The discounted pay-back =3.72 years ( Approximately 3 years 9 months)

4)

Profitability Index = PV of future cash flows/ Initial investment

Profitability Index = (479251+1126664+1365530)/2590000

Profitability Index =1.1472