Problem Set: Cost of Capital andDecision Criteria(Solutions Below)Cost of Capital1. Calculate the cost of equity if stock in a firm has a beta of 1.15.The market risk premium is 8 percent, and T-bills are currentlyyielding 4 percent.2. A bank has an issue of preferred stock with a $6 stated dividendthat just sold for $92 per share. What is the bank's cost ofpreferred stock?3. A firm is trying to determine its cost of debt. The firm has a debtissue outstanding with 12 years to maturity that is quoted at 105percent of its face value of $1,000. The issue makes semiannualpayments and has an coupon rate of 8 percent annually. What isthe pretax cost of debt? If the tax rate is 35 percent, what is theafter-tax cost of debt?4. A firm has a target capital structure of 50 percent common stock,5 percent preferred stock, and 45 percent debt. Its cost of equityis 16 percent, the cost of preferred stock is 7.5 percent, and thecost of debt is 9 percent. The relevant tax rate is 35 percent.What is its WACC? Decision RulesIf r = 10%, determine whether or not to do the following projects(questions 5-9) using each of the five decision criteria:- Payback Period (3 year)- Discounted Payback Period (3 year) - Net Present Value (NPV) Rule - Internal Rate of Return (IRR)- Modified Internal Rate of Return (MIRR) (rRI = 10%)5.0 1 2 3 4-1,0005002002005006.0 1 2 3 4-10,0003,5003,2003,2002,5007.0 1 2 3 4-300250150-2001508.0 1 2 3 4-15,0005,0003,0004,0005,0009.0 1 2 3 4-10,0001,6003,6001,7004,50010. Use the NPV rule to decide on the better project (r = 10%).0 1 2 3 4-10,0003,6003,1002,5004,700-20,0008,3004,9005,2007,200SolutionsNOTE: I include the formulae solutions but you only need to know how to do this on a financial calculator.Cost of Capital1. Calculate the cost of equity if stock in a firm has a beta of 1.15.The market risk premium is 8 percent, and T-bills are currentlyyielding 4 percent.Using the CAPM, we find:RE = .04 + 1.15(.08) = .1320 or 13.20% 2. A bank has an issue of preferred stock with a $6 stated dividendthat just sold for $92 per share. What is the bank's cost ofpreferred stock?The cost of preferred stock is the dividend payment divided bythe price, so:RP = $6/$92 = .0652 or 6.52%3. A firm is trying to determine its cost of debt. The firm has a debtissue outstanding with 12 years to maturity that is quoted at 105percent of face value. The issue makes semiannual paymentsand has an coupon rate of 8 percent annually. What is the pretaxcost of debt? If the tax rate is 35 percent, what is the after-taxcost of debt?P/Y = 2; N = 24; I/Y = 7.37%; PV = 1,050; PMT = -40; FV = -1,000PMT = (1,000 x 0.08)/2 = 40N = 12 x 2 = 24And the after-tax cost of debt is:rD = 0.0737(1 – 0.35) = 0.0479 or 4.79%4. A firm has a target capital structure of 50 percent common stock,5 percent preferred stock, and 45 percent debt. Its cost of equityis 16 percent, the cost of preferred stock is 7.5 percent, and thecost of debt is 9 percent. The relevant tax rate is 35 percent.What is its WACC?Using the equation to calculate the WACC, we find:WACC = 0.50(0.16) + 0.05(0.075) + 0.45(0.09)(1 – 0.35) = 0.1101 or 11.01%Decision RulesIf r = 10%, determine whether or not to do the following projects(questions 5-9) using each of the five decision criteria:a. Payback Period (3 year)b. Discounted Payback Period (3 year) c. Net Present Value (NPV) Rule d. Internal Rate of Return (IRR)e. Modified Internal Rate of Return (MIRR) (rRI = 10%)NOTE: Where applicable, You may also use the financialcalculator functions to sole these problems.5.0 1 2 3 4-1,000500200200500a. Payback Period (3 year)Payback 500 200 200 1,000Decision= + + = <=900Bad Project b. Discounted Payback Period (3 year) ( ) ( )2 3500 200 200Discounted Payback 1,0001.101.10 1.10Decision= + + = <=770.10Bad Project c. Net Present Value (NPV) Rule ( ) ( ) ( )2 3 4500 200 200 500NPV 1,0001.101.10 1.10 1.10$110.60 > 0Decision=- + + + + ==$111.60Good Project d. Internal Rate of Return (IRR)( ) ( ) ( )2 3 4500 200 200 5001,000 011 1 110%DecisionIRRIRR IRR IRRIRR- + + + + =++ + +� = >=15.17%Good Project e. Modified Internal Rate of Return (MIRR) ( )3 24500(1.10) 200(1.10) 200(1.10) 5001,000 0110%DecisionMIRRMIRR+ + +- + =+� = >=12.95%Good Project 6.0 1 2 3 4-10,0003,5003,2003,2002,500a. Payback Period (3 year)Payback 3,500 3,200 3,200 10,000Decision= + + = <=9,900Bad Project b. Discounted Payback Period (3 year) ( ) ( )2 33,500 3,200 3,200Discounted Payback 10,0001.101.10 1.10Decision= + + = <=8,230.65Bad Project c. Net Present Value (NPV) Rule ( ) ( ) ( )2 3 43,500 3,200 3,200 2,500NPV 10,0001.101.10 1.10 1.10-$61.81 < 0Decision=- + + + + ==-$61.81Bad Project d. Internal Rate of Return (IRR)( ) ( ) ( )2 3 43,500 3,200 3,200 2,50010,000 011 1 110%DecisionIRRIRR IRR IRRIRR- + + + + =++ + +� = <=9.70%Bad Project e. Modified Internal Rate of Return (MIRR) ( )3 243,500(1.10) 3,200(1.10) 3,200(1.10) 2,50010,000 0110%DecisionMIRRMIRR+ + +- + =+� = <=9.83%Bad Project 7.0 1 2 3 4-300250150-200150a. Payback Period (3 year)Payback 250 150 200 300Decision= + +- = <=200Bad Project b. Discounted Payback Period (3 year) ( ) ( )2 3250 150 200Discounted Payback 3001.101.10 1.10Decision-= + + = <=200.98Bad Project c. Net Present Value (NPV) Rule ( ) ( ) ( )2 3 4250 150 200 150NPV 3001.101.10 1.10 1.10$3.43 > 0Decision-=- + + + + ==$3.43Good Project d. Internal Rate of Return (IRR) ( ) ( ) ( )2 3 4250 150 200 150300 011 1 110%DecisionIRRIRR IRR IRRIRR-- + + + + =++ + +� = >=10.88%Good Projecte. Modified Internal Rate of Return (MIRR) ( )3 24250(1.10) 150(1.10) 200(1.10) 150300 0110%DecisionMIRRMIRR+ - +- + =+� = >=10.21%Good Project 8.0 1 2 3 4-15,0005,0003,0004,0005,000a. Payback Period (3 year)Payback 5,000 3,000 4,000 15,000Decision= + + = <=12,000Bad Project b. Discounted Payback Period (3 year) ( ) ( )2 35,000 3,000 4,000Discounted Payback 15,0001.101.10 1.10Decision= + + = <=10.030.05Bad Project c. Net Present Value (NPV) Rule ( ) ( ) ( )2 3 45,000 3,000 4,000 5,000NPV 15,0001.101.10 1.10 1.10-$1,554.88 < 0Decision=- + + + + ==-$1,554.88Bad Project d. Internal Rate of Return (IRR) ( ) ( ) ( )2 3 45,000 3,000 4,000 5,00015,000 011 1 110%DecisionIRRIRR IRR IRRIRR- + + + + =++ + +� = <=5.15%Bad Project e. Modified Internal Rate of Return (MIRR)( )3 245,000(1.10) 3,000(1.10) 4,000(1.10) 5,00015,000 0110%DecisionMIRRMIRR+ + +- + =+� = <=7.03%Bad Project 9.0 1 2 3 4-10,0001,6003,6001,7004,500a. Payback Period