What is the present value of a series of payments of $2000 every three years in perpetuity with the first payment made immediately, if the annual rate is 8% per annum?

Question 1

 

Now that they have accumulated a deposit of $40,000 Ed and his partner Susie wish to use the deposit and take out a housing loan to purchase a home. The house costs $725,000. The loan is to be repaid in equal monthly instalments over a term of 25 years.  The interest rate quoted by the bank is an annual effective rate of 5.5%.  Ed has misplaced the paperwork showing the annual nominal rate (j12). Interest is added monthly.

  1. How much is the monthly repayment?
  2. How much interest will be paid in the fifth year?

iii.            How much do Ed and Susie owe the bank immediately before making the 160th repayment?

  1. Provide Ed and Susie with a repayment schedule using excel.

 

(Answers should be accurate to the nearest dollar)

 

Question 2

 

Karine and Arlo are trying to establish a University Fund for their daughter Amelia, who turns 3 today.  They plan for Amelia to withdraw $10,000 on her 18th birthday and $11,000, $12,000 and $15,000 on her subsequent birthdays (19th, 20th and 21st).  They wish to fund these withdrawals with a 10-year annuity, and they intend to make their first deposit one year from today, and expect to earn an average return of 6.5%pa.

  1. How much will Karine and Arlo have to contribute each year to achieve their goal?
  2. Create a schedule showing the cash inflows (including interest) and outflows of this fund.  How much will be in the fund on Amelia’s 16th birthday?

 

(Your answers should be accurate to the nearest dollar)

 

Question 3

 

Stanley has just been advised of a bequest of a lump sum of 111,500 from his Aunt’s will, but it is not due to be available for him for sixteen years (at t = 16 he will receive 111500). Stanley wants to receive some cash earlier than this. He is investigating the purchase of a deferred annuity with the first annual cash flow of the annuity is to be paid at the beginning of year 2 (fifteen cash flows).  Assume that the annuity and the lump sum are of equivalent risk and that j12 = 6.24% pa is the appropriate interest rate (opportunity cost of funds for Stanley). How much is the annual cash flow associated with the annuity?

 

(Accurate to the nearest dollar)

 

Question 4

 

In exchange for a lump sum payment now, Polysuper offers an annual pension over twenty years beginning with a payment of $62,000 at the end of the first year. There are twenty payments in total and the payments will increase at an annual rate of 3%pa. The appropriate opportunity cost of funds is j2 = 9%pa what is the amount of the lump sum needed today to purchase the pension?

 

(Accurate to the nearest dollar)

 

Question 5

 

a)A ninety day bank bill with 90 days to maturity has a price of $98505. What is the effective annual yield implied by this price and maturity? What is the annual nominal yield? Face value is $100,000. Make sure your answers are clearly labelled.

 

  1. b) The All Ordinaries price index opened the year at 5578 and had reached 6013 by the end of the year. What was the rate of return on the index?

 

c)Using the approach covered in your textbook calculate the geometric average annual rate of return over four years given the following annual rates, year 1 = 4.84%, year 2 = 5.99%, year 3 = 6.15%, year 4 = 5.83%.

 

  1. d) Polycorp dividends per share have increased from $6.25 to $13.90 over a six year period. Calculate the annual compounded growth rate in dividends over that period.

 

 (Rates as a percentage accurate to one basis point)

 

Question 6

 

Polycorp Treasury a company in the land of Zanadu is holding a parcel of Zanadu Government Bonds with a face value of $2,000,000.  The bonds were issued six years and nine months ago and still have three years and three months to maturity.  They pay a coupon rate of interest of 6.5% pa, with interest being paid semi-annually. Currently the market yield quoted for Zanadu bonds is 4.12% pa.  The convention in Zanadu financial markets is that the market yield and coupon rate are quoted as annual nominal rates.  What is the current market value of the bonds?

 

(In dollars accurate to three decimal places)

 

Question 7

 

Polycorp has a dividend of $6.00 due in a year’s time and is expected to pay a dividend $6.60 at the end of the second year.  Its dividend is expected to grow at 6.5% pa for the following three year. Dividends are then expected to grow at 3% pa for another two years, after which they are expected to grow at 2%pa forever. Shareholders required return on equity is 10.35% pa.  What is the current price (cum-dividend) of Polycorp shares? D0 is $5.65.

 

(In dollars and cents accurate to the nearest cent)

 

Question 8

 

The required rate of return on the shares in the companies identified below is 12% pa. Calculate the current share price in each case.

 

(a)  The current earnings per share of Alpha Ltd are $3.40. The company does not reinvest any of its earnings. Earnings are expected to remain constant.

(b)  Beta Ltd’s current dividend is $2.35 and dividends are expected to grow at 3% pa indefinitely.

(c)   Gamma Ltd is not expecting to pay dividends for four years, at the end of year five a dividend of $2.39 is planned and dividends are expected to grow at 3.5% pa forever after that.

(d)  Delta limited plans to pay dividends of 1.55, 2.75, and 3.50 at the end of years 3, 4, 5 respectively followed by a dividend of 4.20 pa in perpetuity after that.

 

 (Accurate to the nearest cent)

 

Question 9

You wish to insure your Ferrari.  Mooncorp Insurance has quoted you an annual premium to insure your car of $12915. You are offered a 10% discount if you pay the lump sum immediately. They also offer an alternative payment method.  You can pay the account in full by making 11 equal end-of-the month payments of $1160, rather than the lump sum, with no payment in the first month (ie the first payment is at the end of the second month followed by ten further monthly payments). What is the effective annual opportunity cost of paying monthly?

 

You must provide one complete manual trial calculation of the IRR to demonstrate that you understand the process. Also provide an explanation of this opportunity cost. Failure to follow this instruction will attract a mark of zero.

 

(Accurate to one basis point)

 

Question 10

0 1 2 3 4 5 6 7 8 9 // 12
-2000     -2000     -2000     -2000 // -2000  

(a)   What is the present value of a series of payments of $2000 every three years in perpetuity with the first payment made immediately, if the annual rate is 8% per annum?

 

 

 

 

(b)  Polycorp debentures are selling for $111 (FV = 100) and mature in eight years. The coupon rate is 11%pa. What is the effective annual yield on the debentures?

 

(c)   Polycorp debentures are selling for $103 (FV = 100) and mature in eight years. The coupon rate is 5%pa, with coupons paid quarterly. What is the effective annual yield on the debentures?

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