A regional furniture company is offering either a discount equal to twice the state sales tax or interest-free financing for 60 months. The state sales tax is 6%. What is the effective annual interest rate for financing versus the discount? Assume you are buying $1000 worth of furniture. How will

Question

A regional furniture company is offering either a discount equal to twice the state sales tax or interest-free financing for 60 months. The state sales tax is 6%. What is the effective annual interest rate for financing versus the discount? Assume you are buying $1000 worth of furniture. How will you decide which option to take?

Accepted Answer

TABLE SOLUTION

We set each option’s PW equal to each other. By paying cash, we get a discount of 12% and pay $880 now [= $1000(1 − 0.12)]. If we finance with no interest, the monthly payments are $1000/60 = $16.67. Thus,

1000(1-0.12)=(16.67)(P/A,i,60)

880=16.67(P/A,i,60)

(P/A,i,60)=880/16.67=52.789

From Appendix C,

(P/A,0.25\%,60)=55.653

(P/A,0.50\%,60)=51.726

Interpolating,

Monthly interest rate=0.432%

Nominal annual interest rate=0.432%×12=5.184%

Effective annual interest rate=(1.00432)[latex]^{12} [/latex] -1=0.0531=5.31%

SPREADSHEET SOLUTION

Paying cash is equivalent to financing the purchase at some interest rate. If we pay cash, we will get a discount of 12%, so the present value is $880. If we finance with no interest, monthly payments are $1000/60 = $16.67, so

I	H	G	F	E	D	C	B	A
	Answer	Solve for	FV	PV	PMT	n	i	Problem	1
monthly	0.430%	RATE	0	880	-16.67	60		Exp. 7-6	2
=+H2*12	5.16%	nominal							3
=EFFECT(H3,12)	5.28%	effective							4

The interest-free financing carries an effective annual interest rate of 5.3% relative to paying cash. This rate is much lower than most credit card rates and higher than most savings account rates. How does this rate compare with your MARR?

Question 7.6: A regional furniture company is offering either a discount e...

Related Answered Questions

Verified Answer:

Two machines are being considered for purchase. If the MARR is 10%, which machine should be bought? Use an IRR analysis comparison. ...

Verified Answer:

An engineering student is deciding whether to buy two 1-semester parking permits or an annual permit. The annual parking permit costs $180 due August 15th; the semester permits are $130 due August 15^th and January 15^th. What is the rate of return for buying the annual permit? ...

Verified Answer:

Verified Answer:

An engineer’s employer offers a 401(k) that is invested in the stock market. The engineer deposited $1500 on September 16, 2019, and another $2200 on June 8, 2020. If the account is worth $3840 on August 10, 2020, what annual rate of return has the engineer’s account earned? ...

Verified Answer:

Compare two pumps that are being used for a continuing indefinite requirement. What is the incremental rate of return for buying Pump A, which is longer lasting and more expensive? ...

Verified Answer:

Consider the alternatives in Example 7–11 again, but this time compute the interest rate on the increment (Alt. 1 – Alt. 2) instead of (Alt. 2 – Alt. 1). How do you interpret the results? ...

Verified Answer:

Verified Answer:

Mountain Environmental Consulting may buy some field equipment for $40,000 or lease it for $2500 per month. In either case, the equipment will be replaced in 2 years. The salvage value of the equipment after 2 years is $6000. What is the IRR or cost of the lease? ...

Verified Answer:

Verified Answer: