Financial Management – Assignment Asfa Asfia [18102002] AS B 18 IP 1. 2. 3. 4. 5. What is bond? 5 point What is stock? 5 point What difference between zero coupon bond and coupon bond? 5 point What difference between NPV, IRR, and PI? 5 point The yield to maturity of a $1000 bond with 7% coupon rate, semiannual coupon coupons, and two years to maturity is 7.6% APR, compounded semiannually. What must its price be? 10 point 6. Bond X is a premium bond making annual payments. The bond pays an 8 percent coupon, has a YTM of 6 percent, and has 13 years to maturity. Bond Y is a discount bond making annual payments. This bond pays a 6 percent coupon, has a YTM of 8 percent, and also has 13 years to maturity. If interest rates remain unchanged, what do you expect the price of these bonds to be one year from now? In three years? In eight years? In 12 years? In 13 years? What’s going on here? Illustrate your answers by graphing bond prices versus time to maturity? 15 point 7. If you own 18,000 shares of stock of Nike and it pays a dividend of $0.35 per share, then the price when buy these stocks in 2015 was $18 per share, now the price $20 per share. What is total profit if you sell all your Nike shares now? 15 point 8. Summit systems will pay a dividend of $2.5 this year. If you expect Summit dividend to grow by 4% per year, what is its price per share if the firm equity cost of capital is 9%? 10 point 9. You have been offered a unique investment opportunity. If you invest $10,000 today, you will receive $500 one year from now, $1500 two year from now, and $10,000 three years from now. a. What is the NPV of the opportunity if the cost of capital is 6% per year? Should you take the opportunity? 10 point b. What is the IRR? Bonus ++ c. How long is the profitability index? 10 point 10. For the cash flows below, suppose the firm uses the NPV decision rule. At a required return of 11 percent, should the firm accept this project? What if the required return was 30 percent? 10 point Year 0 1 2 3 Cash Flow -$34,000 16,000 18,000 15,000 Answer 1. Bond is a security sold by governments and corporations to raise money from investors today in exchange for a promised future payment. A bond is normally an interest-only loan, meaning that the borrower will pay the interest every period, but none of the principal will be repaid until the end of the loan. 2. Stock is a security that represents the ownership of a fraction of a corporation. This entitles the owner of the stock to a proportion of the corporation's assets and profits equal to how much stock they own. 3. The difference between zero-coupon bond and coupon (regular) bond a. The zero-coupon bond pays bondholders interest, while the coupon bond does not issue such interest payments, otherwise known as coupons. Instead, zero-coupon bondholders merely receive the face value of the bond when it reaches maturity, while coupon paying bondholders receive both the face value, while also receiving coupons, over the life of the bond. b. Zero-coupon bondholders gain on the difference between the price they pay for the bond and the amount they will receive at the bond's maturity. This can be substantial, because zero-coupon bonds are typically purchased at drastically reduced prices, known as deep discounts, to the bond’s face value. In other words, a zero-coupon bondholder derive financial gain from the difference between the bond’s purchase price and its face value, while the coupon bondholders profit from the regular distribution of interest payments. c. Coupon bonds pay bondholders interest payments throughout the lives of the bonds, while zero-coupon bonds do not issue such interest payments, which are otherwise known as coupons. d. Coupon bonds, however, provide regular interest payments to the bondholder, and at maturity, the bondholder receives the face value of the bond. That can seem to be a bigger advantage, but practically, the yield of zero coupon bonds is usually higher than ordinary bonds. 4. The difference between between NPV, IRR, and PI Point of difference Net Present Internal Rate of Value (NPV) Return (IRR) Meaning The difference The interest rate between the that sets the net present value of a present value of the project’s or cash flows investment’s equal to zero. benefits and the present value of its costs. Profitability Index The ratio of the present value of a project’s future net cash flows to the projet’s initial cash outflow Expressed as We express NPV IRR is expressed in PI is expressed in in the form of the form of the form of a ratio currency returns. percentage returns. Focus NPV focuses on determining whether the investment is generating surplus returns than the expected returns. IRR focuses on determining what is the breakeven rate at which the present value of the future cash flows becomes zero. Discount Rate NPV requires the use of a discount rate which can be difficult to ascertain. IRR doesn’t have PI uses a discount this difficulty since rate to discount the it ‘calculates’ the future cash flows. rate of return. Calculation of Present Value NPV calculates IRR ignores the the present value present value of of future cash future cash flows. flows. 5. Information given : Face Value = $1000 Coupon rate = 7%, semiannual coupons Maturity = 2 years y = 7.6% APR is equal to semiannual rate 3.8% CPN = CPN = Coupon Rate x Face Value Number of Coupon Payments per Year 0.07 x 1000 2 CPN = $35 Thus, the amount of coupon each payment is $35 1 1 πΉπ π = πΆππ × (1 − ) + (1 + π¦)π (1 + π¦)π π¦ PI focuses on determining how many times of the initial investment are we going to get back. The PI method calculates the present value of future cash flows. 1 1 1000 π = 35 × 0.038 (1 − (1.038)2 ) + (1.038)2 = $994,33 Evaluate : Thus, the bond price must be $994,33 6. Information given : Assume face value of bond $1000 Bond X premium, annual Coupon rate = 8% YTM = 6% Maturity = 13 year Bond Y discount, annual Coupon rate = 6% YTM = 8% Maturity = 13 year Manual Calculation : X Corporation bond: Annual coupon Payment for X Bond = $1000 x 8% = $80 P = C(PVIFAR%,t) + $1,000(PVIFR%,t) P0 = $80(PVIFA3%,26) + $1,000(PVIF3%,26) P1 = $80(PVIFA3%,24) + $1,000(PVIF3%,24) P3 = $80(PVIFA3%,20) + $1,000(PVIF3%,20) P8 = $80(PVIFA3%,10) + $1,000(PVIF3%,10) P12 = $80(PVIFA3%,2) + $1,000(PVIF3%,2) P13 = $1,171.05 = $1,167.68 = $1,124.20 = $1,053.46 = $1,018.87 = $1,000 Y Corporation bond: Annual coupon Payment for X Bond = $1000 x 6% = $60 P0 P1 P3 P8 P12 P13 = $30(PVIFA4%,26) + $1,000(PVIF4%,26) = $30(PVIFA4%,24) + $1,000(PVIF4%,24) = $30(PVIFA4%,20) + $1,000(PVIF4%,20) = $30(PVIFA4%,10) + $1,000(PVIF4%,10) = $30(PVIFA4%,2) + $1,000(PVIF4%,2) = $841.92 = $849.28 = $885.07 = $948.46 = $981.48 = $1,000 Excel Calculation : X Corporation bond: Annual coupon Payment for X Bond = $1000 x 8% = $80 P0 P1 P3 P8 P12 P13 Formula PV(6%;0;-80;-1000) PV(6%;1;-80;-1000) PV(6%;3;-80;-1000) PV(6%;8;-80;-1000) PV(6%;12;-80;-1000) PV(6%;13;-80;-1000) Price $1.000,00 $1.018,87 $1.053,46 $1.124,20 $1.167,68 $1.177,05 Y Corporation bond: Annual coupon Payment for X Bond = $1000 x 6% = $60 P0 P1 P3 P8 P12 P13 Formula PV(8%;0;-60;-1000) PV(8%;1;-60;-1000) PV(8%;3;-60;-1000) PV(8%;8;-60;-1000) PV(8%;12;-60;-1000) PV(8%;13;-60;-1000) Price $1.000,00 $981,48 $948,46 $885,07 $849,28 $841,92 Graph : Evaluate : All else held equal, the premium over par value for a premium bond declines as maturity approaches, and the discount from par value for a discount bond declines as maturity approaches. This is called “pull to par.” In both cases, the largest percentage price changes occur at the shortest maturity lengths. As the number of years are increasing, the value of bond X decreasing and the value of the bond Y is increasing. The difference in the present values of bond X and bond Y is because of the different coupon rates and yields. For Bond X the coupon rate is greater than the yield which results in higher bond price and for Bond Y the coupon rate is less than the yield which results in the lower bond price with the increase in the number of years. 7. Information given : Stocks = 18,000 Dividen = $0,35 Price in 2015 = $18 Current Price = $20 Total Return Total profit = $20 - $18 = $2 Or equal to (18,000 x $20) - (18,000 x $18) = $36,000 Evaluate, Thus, total gain is $36,000 8. Information given : Div1 = $2.5 g = 0.04 Cost of capital = 0.09 P0 = Div1 rE−g = $2.5 0.09−0.04 = $50 Evaluate, Thus, the price per share is $50 9. Solution 9.a Information given : NPV = -10,000 + NPV = $202,89 500 (1+0.06)1 + 1,500 (1+0.06)2 + 10,000 (1+0.06)3 Evaluate : Since the NPV is positive we should take it. Solution 9.b IRR (internal rate of return) is The interest rate that sets the net present value of the cash flows equal to zero. Solution 9.c Discounting the cash flow : $500 / (1,06) = $471,70 $1,500 / (1,06)2 = $1,335 3 $10,000 / (1.06) = $8,396.20 = $10,202.9 Profitability index = Present Value of Future Cash Flows/Initial Cash Flow = $10,202.9 / $10,000 = 1,02 Evaluate : Since the PI 1.02 > 1 the company should proceed the project 10. Information given : Year 0 1 2 3 Cash Flow -$34,000 16,000 18,000 15,000 Rate 11% NPV = -34,000 + 16,000 (1+0.11)1 + 18,000 (1+0.11)2 + 15,000 (1+0.11)3 = $5,991.49 Evaluate : Since the NPV is positive the project should be taken Rate 30% NPV = -34,000 + 16,000 (1+0.30)1 + 18,000 (1+0.30)2 + 15,000 (1+0.30)3 = -4,213.93 Evaluate : As the NPV is negative the project should not be taken