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1、 公司理财第四章3.To find the PV of a lump sum, we use:PV = FV / (1 + r)tPV = $15,451 / (1.07)6= $10,295.65PV = $51,557 / (1.15)9= $14,655.72PV = $886,073 / (1.11)18= $135,411.60PV = $550,164 / (1.18)23= $12,223.794.To answer this question, we can use either the FV or the PV formula. Both will give the same
2、 answer since they are the inverse of each other. We will use the FV formula, that is:FV = PV(1 + r)tSolving for r, we get:r = (FV / PV)1 / t 1FV = $307 = $242(1 + r)2;r = ($307 / $242)1/2 1 = 12.63%FV = $896 = $410(1 + r)9;r = ($896 / $410)1/9 1 = 9.07%FV = $162,181 = $51,700(1 + r)15; r = ($162,18
3、1 / $51,700)1/15 1 = 7.92%FV = $483,500 = $18,750(1 + r)30;r = ($483,500 / $18,750)1/30 1= 11.44%5.To answer this question, we can use either the FV or the PV formula. Both will give the same answer since they are the inverse of each other. We will use the FV formula, that is:FV = PV(1 + r)tSolving
4、for t, we get:t = ln(FV / PV) / ln(1 + r) FV = $1,284 = $625(1.06)t;t = ln($1,284/ $625) / ln 1.06 = 12.36 yearsFV = $4,341 = $810(1.13)t;t = ln($4,341/ $810) / ln 1.13 = 13.74 yearsFV = $402,662 = $18,400(1.32)t;t = ln($402,662 / $18,400) / ln 1.32 = 11.11 yearsFV = $173,439 = $21,500(1.16)t;t = ln
5、($173,439 / $21,500) / ln 1.16 = 14.07 years15.For discrete compounding, to find the EAR, we use the equation:EAR = 1 + (APR / m)m 1EAR = 1 + (.08 / 4)4 1= .0824 or 8.24%EAR = 1 + (.18 / 12)12 1= .1956 or 19.56%EAR = 1 + (.12 / 365)365 1 = .1275 or 12.75%To find the EAR with continuous compounding,
6、we use the equation:EAR = eq 1EAR = e.14 1 = .1503 or 15.03%16Here, we are given the EAR and need to find the APR. Using the equation for discrete compounding:EAR = 1 + (APR / m)m 1We can now solve for the APR. Doing so, we get:APR = m(1 + EAR)1/m 1EAR = .1030 = 1 + (APR / 2)2 1APR = 2(1.1030)1/2 1=
7、 .1005 EAR = .0940 = 1 + (APR / 12)12 1APR = 12(1.0940)1/12 1= .0902 EAR = .0720 = 1 + (APR / 52)52 1APR = 52(1.0720)1/52 1= .0696 Solving the continuous compounding EAR equation:EAR = eq 1We get:APR = ln(1 + EAR)APR = ln(1 + .1590)APR = .1476 or 14.76%17. First national bank charges 10.1 percent co
8、mpounded monthly on its business loans.first united bank charges 10.4 percent compounded semiannually .For discrete compounding, to find the EAR, we use the equation:EAR = 1 + (APR / m)m 1So, for each bank, the EAR is:First National: EAR = 1 + (.1010 / 12)12 1 = .1058 or 10.58%First United: EAR = 1
9、+ (.1040 / 2)2 1 = .1067 or 10.67%A higher APR does not necessarily mean the higher EAR. The number of compounding periods within a year will also affect the EAR.第八章1. What is the price of a 10 years ,zero coupon bond paying 1000 at maturity if the ytm is:The price of a pure discount (zero coupon) b
10、ond is the present value of the par. Remember, even though there are no coupon payments, the periods are semiannual to stay consistent with coupon bond payments. So, the price of the bond for each YTM is:a. P = $1,000/(1 + .05/2)20 = $610.27b. P = $1,000/(1 + .10/2)20 = $376.89c. P = $1,000/(1 + .15
11、/2)20 = $235.41 4. Rhiannon corporation has bonds on the market with 13.5 years to maturity ,a ytm of 7.6 percent Here we need to find the coupon rate of the bond. All we need to do is to set up the bond pricing equation and solve for the coupon payment as follows:P = $1,175 = C(PVIFA3.8%,27) + $1,0
12、00(PVIF3.8%,27)Solving for the coupon payment, we get:C = $48.48 Since this is the semiannual payment, the annual coupon payment is:2 $48.48 = $96.96And the coupon rate is the annual coupon payment divided by par value, so:Coupon rate = $96.96 / $1,000 = .09696 or 9.70%6. a japanese company has a bo
13、nd outstanding that sells for 87 percent of its 100.000 par value. The bond has a coupon rate Here we are finding the YTM of an annual coupon bond. The fact that the bond is denominated in yen is irrelevant. The bond price equation is:P = 87,000 = 5,400(PVIFAR%,21) + 100,000(PVIFR%,21) Since we cann
14、ot solve the equation directly for R, using a spreadsheet, a financial calculator, or trial and error, we find:R = 6.56% Since the coupon payments are annual, this is the yield to maturity.10. Say you own an asset that had a total return last year of 14.1 percent The Fisher equation, which shows the
15、 exact relationship between nominal interest rates, real interest rates, and inflation, is:(1 + R) = (1 + r)(1 + h)r = (1 + .141) / (1.068) 1 = .0684 or 6.84%第九章1. the starr co. Just paid a dividend of 1.90 per share on its stock. The dividends are expected to grow at a constant rateThe constant dividend growth model is:Pt = Dt (1 + g) / (R g)So, the price of the stock tod
