Question

Question 4 (Total of 18 marks) Classic Furniture advertises a “One-Year No-Interest Sale” on any purchase over $499. They require a deposit of 10%, with the balance of the purchase price to be paid in 12 equal monthly payments with no interest charged.

(a) What is the cash price equivalent to Classic’s no-interest plan on an item ticketed at $1,000? Assume an interest rate of 11.5% per year compounded monthly. Is this a good deal for a customer? Give a reason.

(b) Flemmings Furniture offers the same no interest plan but requires an establishment fee of $25 payable immediately. Flemmings also charges an account keeping fee of $3.95 per month due with each payment. What is the cash price equivalent to Flemmings’ no-interest plan on an item ticketed at $1,000? Assume the same interest rate as in part (a). Is this a good deal for a customer? Give a reason.

Answer 1

a. Cash price-equivalent is the Present Value of all the monthly payments +the initial 10% deposit.

PV of the equal monthly repayment of ,ie. 1000-(10%*100)= 900/12= 75 at 11.5% p.a. or 11.5%/12 will be:

using the PV of annuity formula

PV=75*(1-(1+(0.115/12))^-12)/(0.115/12)

846.36

So, total cash price-equivalent or PV=846.36+100=

946.36

This is a good deal for the customer as the cash price-equivalent works out to a total of

946.36

less than the full actual/ fair value of

1000

b..Calculating the cash price-equivalent

PV of the equal monthly repayment of ,ie. 1000-25= 975/12= 81.25    PLUS

PV of the 12 account-keeping fee of 3.95   both 11.5% p.a. or 11.5%/12 will be:

using the PV of annuity formula

PV=(81.25+3.95)*(1-(1+(0.115/12))^-12)/(0.115/12)

961.46

So, total cash price-equivalent or PV=961.46+25=

986.46

This is also good deal for the customer as the cash price-equivalent works out to a total of

986.46

less than the full actual/ fair value of

1000

But option b. is costlier than a.

as ,in the former,

amt. paid immediately( 25) is less & staggered monthly payments(81.25+3.95)=85.2 are more

whereas under option a.

amt. paid immediately( 100) is more & staggered monthly payments (75) are less.

Interest is in-built in the options.

So, option a. has less interest

Option. B. has more interest element.