Question

	JB HiFi (JBH)
Instalment per month ($’000s)	$32.9
Annual total revenue ($millions)1	$7,095.3
Annual growth in total revenue2	16.14%
Loan A (APR, compounding frequency)	4.62%, semi- annually
Loan B (APR, compounding frequency)	4.52%, quarterly
Loan C (APR, compounding frequency)	4.24%, daily3
Property cost	$691,000
7 year bond annual coupon rate	5.85%
7 year bond current price	$99.95
5 year bond required rate of return	4.85%

TVM and bond valuation questions (1 mark each):

a.            Your case company has just made a large sale on an instalment contract. The contract requires the customer to pay your case company the amount shown in Table 1 (JBH)at the end of every month for 5 years. Your case company would like the cash now for an investment and so has asked its bank to discount the instalment contract and pay it the discounted value. The bank will discount the contract at 6% APR, compounded monthly. How much cash will your case company receive from the bank?

b.            Your company has annual operating revenue as shown in Table 1. Assume this revenue will grow continuously at the annual rate shown in Table 1. What is your prediction for annual operating revenue in 7 years?

c.            Your company needs to borrow funds and has several options available to it, Loans A, B and

C. The interest rates (APR) for these options are given in Table 1. What is the EAR of the loan option the company should choose?

d.            Your company is buying new property for the amount given in Table 1. To finance this, the company’s bank has offered an amortised loan at 3.65% APR, quarterly compounding, with 11 years of quarterly payments. What quarterly payment will the company have to make on this loan? Assume that the entire property cost is financed and that payments are made at the end of each period.

e.            Your company has an issue of $100 par value annual coupon bonds with 7 years remaining until maturity. The annual coupon rate is given in Table 1, along with the current price of the bonds. What is the yield to maturity on the bonds?

f.            Your company has an issue of $1,000 par value bonds that offer a 8% coupon rate paid semi- annually. The bonds have 5 years remaining until maturity. The market’s required return on these bonds is given in Table 1. What is the amount of each coupon payment?

Answer 1

Part (a): The amount received on discounting installments is the present value of annuity arrived at $17,017,709.49 as follows:

1 Present Value of Annuity Payments at the end of each period 2 3 Present value of annuity is calculated using the formula PVA=P*{[1-(1+r)^-n]/r]} 4 Where P= Periodical payments, 5 n= Number of payments. 6 r=Rate of interest per period in decimals 7 All amounts in $ 8 Given that 9 Periodical payments (P)= 329000 No. of years (N)= 10 Rate of interest (% p.a)=R= 6 No. of payments a year (t)= 11 12 Calculations: 13 Formula Cell reference Value 14 Interest rate per period in decimals (r)= R/(100*t) D10/(100*G10) 0.005 15 No. of periods (n)= Nit G9*G10 (1+r)= 1+G14 1.005 17 (1+r)^-n= G164-G15 0.741372196 18 [1-(1+r)^-n)= 1-G17 0.258627804 19 [1-(1+r)^-n]/r= G18/614 51.72556075 20 Present value of annuity PV= P*{[1-(1+r)^-n]/r]} D9*G19 17017709.49 21 Rounded to $17,017,709.49 22 60 16

Part (b):Annual operating income in 7 years is the future value of current operating income, arrived at $ 20,222.90 Million as follows:

1 Future Value 2 3 Future value of an amount is calculated using the formula FV=P(1+r)^n 4 Where P= Principal (Presen Value), 5 n= Number of payments. 6 r= Rate of interest per period in decimals All amounts in Million $ Given that 9 Present Value (P)= 7095.3 No. of years (N)= 10 Rate of interest (% p.a)=R= 16.14 No. of times compounded a year (t) = 11 12 Calculations: 13 Formula Cell reference Value 14 Interest rate per period in decimals (r)= R/(100*t) D10/(100*G10) 0.1614 15 No. of periods (n)= N*t G9*G10 (1+r)= 1+G14 1.1614 (1+r)^n= G16^G15 2.850183043 18 Future value FV= P*(1+r)^n D9*G17 20222.90374 19 Rounded to 20,222.90 20 16 17

Part (c):

EAR of various APRs given are as follows:

APR and compounding frequency	EAR
4.62% Semi annually	4.673361%
4.52% Quarterly	4.597193%
4.24% Daily	4.330915%

Details as follows:

R F4 fx =1*(1+F1/F3)^F3 B C 1 APR 2 Frequency of compounding 3 Number of times compounded a yeart 4 Future value of $ 1 FV =1*(1+R/t)^t 5 Equivalent Annual Rate EAR FV-1 D E F 4.62% 4.52% 4.24% Semi annually Quarterly Daily 4 365 1.04673361 1.04597193 1.043309151 0.04673361 0.04597193 0.043309151 6

Part (d):

Quarterly payment on the loan of $691,000 (cost of property is $ 19,138.23 as follows:

8 A B C D 1 Equated Quarterly Installments (EQI) Payments at the end of each period 3 EQI is calculated using the formula EQI=[P*r*(1+r)^n]/((1+r)^n)-1 4 Where P= Principal (loan amount), 5 n= Number of installments. 6 r= Rate of interest per quarter in decimals. 7 All amounts in $ Given that 9 Principal (loan amount) (P)= L 691000 No. of years (N)= 10 Rate of interest (% p.a)=R= L 3.65 No. of quarters (n)= 11 12 Calculations: 13 Formula Cell reference Value 14 Interest rate per quarter in decimals (r )= R/(100*4) D10/(100*4) 0.009125 15 No. of quarter (n)= N*12 G9*12 44 16 (1+r)= 1+G14 1.009125 (1+r)^n= G16^G10 1.491346233 [(1+r)^n]-1= G17-1 0.491346233 P*r*(1+r)^n= D9*G14*G17 9403.497255 20 Equated Quarterly Insallments )= [P*r*(1+r)^n]/[(1+r)^n)-1 G19/618 19138.23007 Rounded to | $19,138.23 18 Imants =

Part (e); YTM is calculated at 5.87675266% using the RATE function of Excel as follows:

D Function FV $100 5.85% Annual Assumed for =RATE(E7,E8,29*-1,E2) C 1 Formula Cell ref. 2 Face Value (FV) Given 3 Coupon rate (R) Given 4 Interest frequency Given 5 Number of coupon payments a year (n) t 6 Time to maturity (no. of years) (N) Given 7 Number of future coupon payments (t) N*t E6*E5 8 Amount of coupon payment FV*R E2*E3 9 Price (Present value) Given 10 Interest rate (YTM) Nper PMT PV RATE $5.85 $99.85 5.87675266% 11 12

Part (f) Amount of coupon payment is Par Value* Coupon Rate/ No. of payments a year.

In the given case,

Par Value= $1,000. Coupon Rate= 8%. Coupon payment frequency= Semi annual. Hence number of payments a year=2.

Therefore, amount of each coupon payment= $1,000*8%/2 = $1,000*4% = $40