Fight Finance

Question 53  bond pricing

A two year Government bond has a face value of $100, a yield of 2.5% pa and a fixed coupon rate of 0.5% pa, paid semi-annually. What is its price?

(a) 90.6421

(b) 95.1524

(c) 95.2055

(d) 96.1219

(e) 103.9751

Question 156  APR, effective rate

A 2 year government bond yields 5% pa with a coupon rate of 6% pa, paid semi-annually.

Find the effective six month rate, effective annual rate and the effective daily rate. Assume that each month has 30 days and that there are 360 days in a year.

All answers are given in the same order:

##r_\text{eff semi-annual}##, ##r_\text{eff yrly}##, ##r_\text{eff daily}##.

(a) 0.024695, 0.05, 0.000136.

(b) 0.025, 0.050625, 0.000137.

(c) 0.029563, 0.06, 0.000162.

(d) 0.03, 0.06, 0.000167.

(e) 0.03, 0.0609, 0.000164.

Question 256  APR, effective rate

A 2 year corporate bond yields 3% pa with a coupon rate of 5% pa, paid semi-annually.

Find the effective monthly rate, effective six month rate, and effective annual rate.

##r_\text{eff monthly}##, ##r_\text{eff 6 month}##, ##r_\text{eff annual}##.

(a) 0.002466, 0.014889, 0.03.

(b) 0.002485, 0.015, 0.030225.

(c) 0.004074, 0.024695, 0.05.

(d) 0.004124, 0.025, 0.050625.

(e) 0.004167, 0.025, 0.05.

Question 298  interest only loan

A prospective home buyer can afford to pay $2,000 per month in mortgage loan repayments. The central bank recently lowered its policy rate by 0.25%, and residential home lenders cut their mortgage loan rates from 4.74% to 4.49%.

How much more can the prospective home buyer borrow now that interest rates are 4.49% rather than 4.74%? Give your answer as a proportional increase over the original amount he could borrow (##V_\text{before}##), so:

###\text{Proportional increase} = \frac{V_\text{after}-V_\text{before}}{V_\text{before}} ###

Assume that:

• Interest rates are expected to be constant over the life of the loan.

• Loans are interest-only and have a life of 30 years.

• Mortgage loan payments are made every month in arrears and all interest rates are given as annualised percentage rates compounding per month.

(a) 0.055679

(b) 0.029631

(c) 0.029547

(d) 0.006245

(e) 0.0025

Question 328  bond pricing, APR

A 10 year Australian government bond was just issued at par with a yield of 3.9% pa. The fixed coupon payments are semi-annual. The bond has a face value of $1,000.

Six months later, just after the first coupon is paid, the yield of the bond decreases to 3.65% pa. What is the bond's new price?

(a) $1,000

(b) $1,019.9181

(c) $1,033.8330

(d) $1,052.7005

(e) $1,060.5226

Question 520  NPV, DDM

The following cash flows are expected:

• Constant perpetual yearly payments of $70, with the first payment in 2.5 years from now (first payment at t=2.5).
• A single payment of $600 in 3 years and 9 months (t=3.75) from now.

What is the NPV of the cash flows if the discount rate is 10% given as an effective annual rate?

(a) $875.549502

(b) $921.135446

(c) $971.279985

(d) $1,026.438978

(e) $1,119.690058

Question 652  future, continuously compounding rate

An equity index is currently at 5,200 points. The 6 month futures price is 5,300 points and the total required return is 6% pa with continuous compounding. Each index point is worth $25.

What is the implied dividend yield as a continuously compounded rate per annum?

(a) 5.7145% pa

(b) 4.0952% pa

(c) 3.8096% pa

(d) 2.1904% pa

(e) 1.9048% pa

Question 748  income and capital returns, DDM, ex dividend date

A stock will pay you a dividend of $2 tonight if you buy it today.

Thereafter the annual dividend is expected to grow by 3% pa, so the next dividend after the $2 one tonight will be $2.06 in one year, then in two years it will be $2.1218 and so on. The stock's required return is 8% pa.

What is the stock price today and what do you expect the stock price to be tomorrow, approximately?

(a) $40 tonight and $38 tomorrow.

(b) $41.2 tonight and $39.2 tomorrow.

(c) $41.2 tonight and $43.2 tomorrow.

(d) $43.2 tonight and $41.2 tomorrow.

(e) $45.2 tonight and $43.2 tomorrow.

Question 761  NPV, annuity due, no explanation

The phone company Optus have 2 mobile service plans on offer which both have the same amount of phone call, text message and internet data credit. Both plans have a contract length of 24 months and the monthly cost is payable in advance. The only difference between the two plans is that one is a:

• 'Bring Your Own' (BYO) mobile service plan, costing $80 per month. There is no phone included in this plan. The other plan is a:
• 'Bundled' mobile service plan that comes with the latest smart phone, costing $100 per month. This plan includes the latest smart phone.

Neither plan has any additional payments at the start or end. Assume that the discount rate is 1% per month given as an effective monthly rate.

The only difference between the plans is the phone, so what is the implied cost of the phone as a present value? Given that the latest smart phone actually costs $600 to purchase outright from another retailer, should you commit to the BYO plan or the bundled plan?

(a) $480, so the bundled plan is best.

(b) $462.94, so the BYO plan is best.

(c) $429.12, so the bundled plan is best.

(d) $424.87, so the BYO plan is best.

(e) $420.66, so the bundled plan is best.

Question 798  idiom, diversification, market efficiency, sunk cost, no explanation

The following quotes are most closely related to which financial concept?

• “Opportunity is missed by most people because it is dressed in overalls and looks like work” -Thomas Edison
• “The only place where success comes before work is in the dictionary” -Vidal Sassoon
• “The safest way to double your money is to fold it over and put it in your pocket” - Kin Hubbard

(a) The efficient markets hypothesis.

(b) Time value of money.

(c) Separation of the investment and financing decisions.

(d) Diversification.

(e) Sunk costs.