第一次作业答案(1-4) Question 1 The present value of E100 received five years from now PV= ￡62.09 +0.10) b. The present value of f1000 received 60 years from now is P1000 ￡3.28 1+0.10) c. The present value E100 received each year beginning one year from now and ending 0 years from now is P=100-100 (1+0.10 ￡61446 0.100.10 d. The present value of f100 received each year beginning one year from now and continuing forever is PV= ￡1000.00 Question 2 1EAR={1+08)2 1=8.30% ii. EAR=1+ 0.08 1=8.16% iii. EAR=1+ 0.08 1=8.33% 365 EAR=e0=8.33% b. The interest payment per quarter on a E10,000 deposit ￡l00(12031)2=30455 The value of f10 000 after six months is ￡10,000×14012 4)=10609 d. Assume that the equivalent interest rate(APR)with quarterly compounding is r, then 0.12 r=11.8252% 4 Therefore, the quarterly interest payment on a f10,000 deposit is ￡10.000 0.118252 =￡29563 C Gary Xu AcF2 14 Princip les of finance
© Gary Xu AcF214 Principles of Finance 1 第一次作业答案（1－4） Question 1 a. The present value of £100 received five years from now is ( ) £62.09 1 0.10 100 5 = + PV = b. The present value of £1000 received 60 years from now is ( ) £3.28 1 0.10 1000 60 = + PV = c. The present value £100 received each year beginning one year from now and ending 10 years from now is (1 0.10) £614.46 0.10 100 0.10 100 10 = − + = − PV d. The present value of £100 received each year beginning one year from now and continuing forever is £1000.00 0.10 100 PV = = Question 2 a. i. 1 8.30% 12 0.08 1 12 − = EAR = + ii. 1 8.16% 2 0.08 1 2 − = EAR = + iii. 1 8.33% 365 0.08 1 365 − = EAR = + iv. 8.33% 0.08 EAR = e = b. The interest payment per quarter on a £10,000 deposit £10,000 ( 1) £304.55 0.12 0.25 − = e c. The value of £10,000 after six months is £10,609 4 0.12 £10,000 1 2 = + d. Assume that the equivalent interest rate (APR) with quarterly compounding is r, then 4 2 2 0.12 1 4 1 = + + r r =11.8252% Therefore, the quarterly interest payment on a £10,000 deposit is £295.63 4 0.118252 £10,000 =
a. The price of the bond with face value of f100 7 P 1+0.08 +0.0 0.080.08 08)° =f93.29 The equivalent yield-to-maturity(APR)with semi-annual compound ing is 1.08→r=7.8461% The price of the bond with face value of f100 if the yield-to-maturity is 8% per year is 3.5 3.5 3.5 P 1+00392305(+0392305)(+0392305)0(1+00392305) 3.5 3.5 0.03923050.0392305 +0392305)2+100×(1+0.0392305)20 The te, g, Is g=(1-02)×017=136% b. The intrinsic value of the stock is 5×0.20 P ￡7143 0.15-0.136 The expected price a year from now is P1=P0×(+g)=￡81.14 5×02 50 0.15 Therefore, the expected turn on the firms new investments is 0.13=0.8 1r-0.136=50=r=156 50→h=0.29 (1-b) C Gary Xu AcF2 14 Princip les of Finance 2
© Gary Xu AcF214 Principles of Finance 2 Question 3 a. The price of the bond with face value of £100 is ( ) ( ) ( ) ( ) ( ) £93.29 1 0.08 100 1 0.08 0.08 7 0.08 7 1 0.08 100 1 0.08 7 1 0.08 7 1 0.08 7 1 0 1 0 0 2 1 0 1 0 = + + = − + + + + + + + + + = − p b. The equivalent yield-to-maturity (APR) with semi-annual compounding is 1.08 2 1 2 = + r r = 7.8461% The price of the bond with face value of £100 if the yield-to-maturity is 8% per year is ( ) ( ) ( ) ( ) ( ) £94.21 1 0.0392305 100 1 0.0392305 0.0392305 3.5 0.0392305 3.5 1 0.0392305 100 1 0.0392305 3.5 1 0.0392305 3.5 1 0.0392305 3.5 2 0 2 0 0 2 2 0 2 0 = = + + + + + + + + + + + + = − − p Question 4 a. The growth rate, g, is g = (1− 0.2)0.17 =13.6% b. The intrinsic value of the stock is £71.43 0.15 0.136 5 0.20 0 = − p = c. The expected price a year from now is p1 = p0 (1+ g) = £81.14 d. i. 50 0.15 5 0.2 = − g g = 13% Therefore, the expected turn on the firm’s new investments is * 0.13 = 0.8 r 16.25% * r = ii. 50 0.136 5 0.2 = − r r =15.6% iii. ( ) 50 0.15 0.17 1 5 = − − h h h = 0.29