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HQ Ltd. purchased a used truck from Trans Auto Sales Inc. HQ paid a $4,500 down...

Question:

HQ Ltd. purchased a used truck from Trans Auto Sales Inc. HQ paid a $4,500 down payment and signed a note that calls for 36 payments of $1,047.00 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. (For calculation purposes, use 5 decimal places as displayed in the factor table provided. Round final answers to 2 decimal places, e.g. 5,275.25.)

1.What was the purchase price of the used truck excluding the incentive given?

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

3. 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.

  • a. 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.
  • b. 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.

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

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


Answers

Assuming 4% interest rate is on montly basis.

1. Purchase price of Truch excluding incentive = $24,296.97

Month Payment Discount Factor @4% Present Vlaue
0 $ 4,500.00 1 $            4,500.00
1 $ 1,047.00                             0.96154 $            1,006.73
2 $ 1,047.00                             0.92456 $                968.01
3 $ 1,047.00                             0.88900 $                930.78
4 $ 1,047.00                             0.85480 $                894.98
5 $ 1,047.00                             0.82193 $                860.56
6 $ 1,047.00                             0.79031 $                827.46
7 $ 1,047.00                             0.75992 $                795.63
8 $ 1,047.00                             0.73069 $                765.03
9 $ 1,047.00                             0.70259 $                735.61
10 $ 1,047.00                             0.67556 $                707.32
11 $ 1,047.00                             0.64958 $                680.11
12 $ 1,047.00                             0.62460 $                653.95
13 $ 1,047.00                             0.60057 $                628.80
14 $ 1,047.00                             0.57748 $                604.62
15 $ 1,047.00                             0.55526 $                581.36
16 $ 1,047.00                             0.53391 $                559.00
17 $ 1,047.00                             0.51337 $                537.50
18 $ 1,047.00                             0.49363 $                516.83
19 $ 1,047.00                             0.47464 $                496.95
20 $ 1,047.00                             0.45639 $                477.84
21 $ 1,047.00                             0.43883 $                459.46
22 $ 1,047.00                             0.42196 $                441.79
23 $ 1,047.00                             0.40573 $                424.80
24 $ 1,047.00                             0.39012 $                408.46
25 $ 1,047.00                             0.37512 $                392.75
26 $ 1,047.00                             0.36069 $                377.64
27 $ 1,047.00                             0.34682 $                363.12
28 $ 1,047.00                             0.33348 $                349.15
29 $ 1,047.00                             0.32065 $                335.72
30 $ 1,047.00                             0.30832 $                322.81
31 $ 1,047.00                             0.29646 $                310.39
32 $ 1,047.00                             0.28506 $                298.46
33 $ 1,047.00                             0.27409 $                286.98
34 $ 1,047.00                             0.26355 $                275.94
35 $ 1,047.00                             0.25342 $                265.33
36 $ 1,047.00                             0.24367 $                255.12
Total $          24,296.97

2. Incentive of 2 month's payment $1047 p.m. need to be transfered to profit and loss and debit Trans Auto Sales Inc. account at the end of each waiver month.

3.

Present value of the 34 payments of $1,033.34 = $17,822.23

a. Present value of the 34 payments as of the end of the second month following the purchase of the used truck = $19,276.52

Month Payment Discount Factor @4% Present Vlaue
3 $ 1,047.00                             0.96154 $            1,006.73
4 $ 1,047.00                             0.92456 $                968.01
5 $ 1,047.00                             0.88900 $                930.78
6 $ 1,047.00                             0.85480 $                894.98
7 $ 1,047.00                             0.82193 $                860.56
8 $ 1,047.00                             0.79031 $                827.46
9 $ 1,047.00                             0.75992 $                795.63
10 $ 1,047.00                             0.73069 $                765.03
11 $ 1,047.00                             0.70259 $                735.61
12 $ 1,047.00                             0.67556 $                707.32
13 $ 1,047.00                             0.64958 $                680.11
14 $ 1,047.00                             0.62460 $                653.95
15 $ 1,047.00                             0.60057 $                628.80
16 $ 1,047.00                             0.57748 $                604.62
17 $ 1,047.00                             0.55526
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