第一次作业答案

第一次作业答案（1－4）

Question 1

a. The present value of £100 received five years from now is

()

09.62£10.01100

5=+=PV b. The present value of £1000 received 60 years from now is ()28.3£10.01100060=+=PV

c. The present value £100 received each year beginning one year from now and ending 10 years from now is

()46.614£10.0110.0100

10.0100

10=+-=-PV

d. The present value of £100 received each year beginning one year from now and continuing forever is

00.1000£10.0100

==PV

Question 2

a. i.

%30.811208.0112=-⎪⎭⎫ ⎝⎛+=EAR ii.

%16.81208.012=-⎪⎭⎫ ⎝⎛+=EAR iii. %

33.8136508.01365=-⎪⎭⎫ ⎝⎛+=EAR iv. %33.808.0==e EAR b.

The interest payment per quarter on a £10,000 deposit ()55.304£1000,10£25.012.0=-⨯⨯e c. The value of £10,000 after six months is

609,10£412.01000,10£2=⎪⎭⎫ ⎝⎛+⨯

d. Assume that the equivalent interest rate (APR) with quarterly compounding is r , then

24212.0141⎪⎭⎫ ⎝⎛+=⎪⎭⎫ ⎝⎛+r ⇒ %8252.11=r

Therefore, the quarterly interest payment on a £10,000 deposit is 63.295£4118252

.0000,10£=⨯

Question 3

a. The price of the bond with face value of £100 is

()()()()()29

.93£08.0110008.0108.0708.0708.0110008.01708.01708.0171010101020=++⎥⎦

⎤⎢⎣⎡+-=++++++++=

- p

b. The equivalent yield-to-maturity (APR) with semi-annual compounding is

08.1212=⎪⎭⎫ ⎝⎛+r ⇒ %8461.7=r

The price of the bond with face value of £100 if the yield-to-maturity is 8% per year is

()()()()()21

.94£0392305

.011000392305.010392305.05.30392305.05

.30392305.011000392305.015.30392305.015.30392305.015.32020202020=+⨯+++=++++++++=

-- p

Question 4

a. The growth rate, g , is

()%6.1317.02.01=⨯-=g

b. The intrinsic value of the stock is

43.71£136.015.020.050=-⨯=p

c.

The expected price a year from now is ()14.81£101=+⨯=g p p

d. i. 5015.02.05=-⨯g ⇒ %13=g

Therefore, the expected turn on t he firm’s new investments is

*8.013.0r ⨯= ⇒ %25.16*=r ii. 50136.02

.05=-⨯r ⇒ %6.15=r

iii. ()50117.015.05=-⨯-⨯h h

⇒ 29.0=h