Question

HQ Ltd. purchased a used truck from Trans Auto Sales Inc. HQ paid a $4,000 down payment and signed a note that calls for 36 payments of $1,033.34 at the end of each month. The stated rate of interest in the note is 4%. As an incentive for entering into the contract, Trans has agreed to forgive the first two payments under the lease.

Instructions

a.  What was the purchase price of the used truck excluding the incentive given? To calculate, use (1) a financial calculator or (2) Excel function PV.

b.  What effect, if any, does the forgiveness of the first two payments have on the purchase price of the truck?

c.  Calculate the present value of the 34 payments of $1,033.34 that will be made by HQ for payments 3 to 36 inclusive. You will need to perform two steps.

• 1.Calculate the present value of the 34 payments as of the end of the second month following the purchase of the used truck. Use (a) a financial calculator or (b) Excel function PV.
• 2.Take the result from the first calculation and calculate the present value as of the date of purchase. Use (a) a financial calculator or (b) Excel function PV.

d.  What amount should HQ use to record the purchase of the truck?

e.  What amount of interest should be accrued at the end of the first month following the purchase?

Answer 1

a.

To calculate the present value of the future cash payments under the note:

1.

Using a financial calculator:

PV	?	Yields $ 35,000.23
I	.3333%1
N	36
PMT	$ (1,033.34)
FV	$ 0
Type	0

1 (4% / 12 months)

2.

Using Excel: =PV(rate,nper,pmt,fv,type)

Function Arguments ? X PV Rate 0.003333 ti = 0.003333 Nper 36 til 1 = 36 Pmt -1033.34 ↑ -1033.34 Fv 0 0 Type d 1 = 0 = 35000.22872 Returns the present value of an investment: the total amount that a series of future payments is worth now. Type is a logical value: payment at the beginning of the period = 1; payment at the end of the period = 0 or omitted. Formula result = 35,000.23 Help on this function OK Cancel

Result: $35,000.23

Purchase price of the used truck:

PV of future cash flows $35,000.23

Down payment 4,000.00

Total purchase price $39,000.23

b.

The forgiveness of the first two monthly payments affects the transaction price of the used truck. Time value of money must be imputed in the delayed start of payments to arrive at the present value of the future cash flows under the terms of the note. Interest accrues from the date of purchase and must be recognized each month as an expense although the cash flows of the monthly payments are delayed two months.

c.

To calculate the present value of the future cash payments under the note involves two steps:

Step 1: calculate the present value of the annuity of 34 payments of $1,033.34.

(a) Using a financial calculator:

PV	?	Yields $ 33,163.80
I	.3333%1
N	34
PMT	$ (1,033.34)
FV	$ 0
Type	0

1 (4% / 12 months)

(b) Using Excel: =PV(rate,nper,pmt,fv,type)

Function Arguments ? X PV Rate .003333 1 = 0.003333 Nper 34 1 = 34 Pmt -1033.34 = -1033.34 + + + + FV 0 Type o 1 = 0 = 33163.80493 Returns the present value of an investment: the total amount that a series of future payments is worth now. Type is a logical value: payment at the beginning of the period = 1; payment at the end of the period = 0 or omitted. Formula result = 33,163.80 Help on this function OK Cancel

Result: $33,163.80

2.

The second step is to bring the present value of $33,163.80 to the date of purchase using an annual rate of 4%.

(a) Using a financial calculator:

PV	?	Yields $ 32,944.17
I	.6667%1
N	1
PMT	$ 0
FV	$ (33,163.80)
Type	0

1 (4% x 2/12 months)

(b) Using Excel: =PV(rate,nper,pmt,fv,type)

Function Arguments ? X PV Rate 0.006667 1 = 0.006667 1 " tilt Pmt 0 = 0 Nper 1 1 = 0 Fv -33163.8 = -33163.8 Type o 1 = 32944.16128 Returns the present value of an investment: the total amount that a series of future payments is worth now. Type is a logical value: payment at the beginning of the period = 1; payment at the end of the period = 0 or omitted. Formula result 32,944.16 Help on this function OK Cancel

Result: $32,944.16

d.

Purchase price of the used truck:

PV of future cash flows $32,944.16

Down payment    4,000.00

Total purchase price $36,944.16

e.

The amount of interest accrued at the end of the first month following the purchase will be:

$32,944.16 x .04 x 1/12 = $109.81