Question

Time Value of Money:  

(a) Temina Co leased a cake making factory on September 30, 2016. Terms of the lease require Temina to make 10 annual lease payments of $55,000 with the first payment due immediately. Accounting standards require the company to record a lease liability when recording this type of lease. Assuming an 8% interest rate, at what amount should Temina record the lease liability on September 30, 2016, before the first payment is made?

(b) Ethan Sereti wants to accumulate $100,000 to be used for launching his art business. He would like to have the amount available on December 31, 2021 when he turns 36. Assume that the funds will accumulate in an account paying 10% interest compounded semiannually.

Required: Answer each of the following independent questions.

1. If Ethan were to deposit a single amount, how much would he have to invest on December 31, 2018?

2. If Ethan were to make five equal deposits on each December 31, beginning on December 31, 2018, what is the required amount of each deposit?

(c) McDonald purchased a new boat for $20,000. McDonald made a cash down payment of $5,000 and agreed to pay the remaining balance in 30 monthly installments, beginning one month from the date of purchase. Financing is available at a 10% annual interest rate.

Required: Calculate the amount of the required monthly payment.

(d) Malaika’s Toy Makers Inc needs to acquire a gadget to be used in its manufacturing process. The gadget under consideration can be used for 10 years and then sold for $10,000 at the end of its useful life. A close by manufacturer of the gadget has presented Malaika with the following options:

1. Buy machine. The machine could be purchased for $160,000 in cash. All maintenance and insurance costs, which approximate $5,000 per year, would be paid by Malaika.

2. Lease machine. The machine could be leased for a 10-year period for an annual lease payment of $25,000 with the first payment due immediately. All maintenance and insurance costs will be paid for by the manufacturer and the machine will revert back to the manufacturer at the end of the 10-year period.

Required: Assuming that a 10% interest rate properly reflects the time value of money in this situation and that all maintenance and insurance costs are paid at the end of each year, determine which option Malaika should choose.

Answer 1

Answer to Question a)

PV of lease payment = PV factor for each year X Annual lease payment.

PV factor for each year = 1/(1+i)ⁿ, Where i = assumed interest rate = 8%, n = corresponding number of each year, for example, now or 30th september = 0, next year = 1 etc....,

year	PV factor	Annual lease rent	PV of Annual Lease rent
0	1	55000	55000
1	0.925925926	55000	50925.92593
2	0.85733882	55000	47153.63512
3	0.793832241	55000	43660.77326
4	0.735029853	55000	40426.6419
5	0.680583197	55000	37432.07584
6	0.630169627	55000	34659.32948
7	0.583490395	55000	32091.97174
8	0.540268885	55000	29714.78865
9	0.500248967	55000	27513.69319
Amount to be recognised as lease liability immediately before payment of 1st Installment			$398,578.8351

Answer to question b),

1) Amount will be invested in 2018 December till 2021 December, Which means for 3 years at begining. Interest rate is 10%,

So if he invests $1, it will be at 2021 December worth $1.331. if he wants to get $100,000, devide this $100,000 by accumulated amount of $1, so $100,000/1.331 = $75,131.4800901578. He is to be invested single sum of $75131.48.

2) If he wants to invest annually, we have to get annuity for 3 years at beginning,

Normally formula of annuity is for investments made at year end, here investing at year0, which means at beginnig, so we have to add 1 with 'n' in formula, formula is (((1+i)ⁿ)-1)/i, here n = number of year = 3, but we have to add1, so n will be 4, and i will be 10% or 0.1. so (1.1⁴)-1)/0.1. and deduct 1 from the annuity received from formula. we will get 4.641 from formula, so deduct 1 , then the annuity for 3 years from beginning will be 3.641. and devide the $100,000 by this annuity, so $100,000/3.641 = $27,464.9821477616. He is to be invested $27464.98 per year.

Answer to Question c)

Equal monthly installment = Out standing amount / Monthly PV annuity factor.

Monthly PV annuity factor = (((1+i)ⁿ)-1) /((1+i)ⁿ)(i) =

where i = monthly interest rate, which is = 10%/12 = 0.8333% or 0.0083333 n = number of months = 30.

= (((1.0083333)³⁰)-1) /(((1.0083333)³⁰)(i)), = 26.4480918931177

out standing Amount will be $20,000 - $5,000 = $15,000.

after solving the formula, we will get 26.4480918931177 as Monthly PV annuity factor

So monthly Amount of repayment = $15,000/26.4480918931177,

567.148664660504, monthly repayment will be $567.15.

Answer for quetion d),

Here Malaika will select option which will give minimum PV of outflow.

PV of Buying the asset will be Buyin g Cost + PV of Maintenance cost - PV of salvage value.

PV of

maintenance cost = PV factor X Annual maintenance cost.

PV of salvage value = PV factor for year 10 x PV of salvage value,

PV factor = 1/(1+i)ⁿ, n = corresponding number of the years, i = 10% or 0.1,

year	PV Factor	Maintenance Cost PA	PV of Maintenance cost
1	0.909090909	$                        5,000.00	$                             4,545.45
2	0.826446281	$                        5,000.00	$                             4,132.23
3	0.819616417	$                        5,000.00	$                             4,098.08
4	0.812842997	$                        5,000.00	$                             4,064.21
5	0.806125552	$                        5,000.00	$                             4,030.63
6	0.799463622	$                        5,000.00	$                             3,997.32
7	0.792856747	$                        5,000.00	$                             3,964.28
8	0.786304472	$                        5,000.00	$                             3,931.52
9	0.779806345	$                        5,000.00	$                             3,899.03
10	0.773361921	$                        5,000.00	$                             3,866.81
		Total PV	$                           40,529.58

PV of salvage value = 10th year PV factor X Salvage Value = $10,000 X 0.773361921 = $7,733.61921.

So PV of Buying the Machine = $160,000+$40,529.58 - $7,733.62 = $192,795.956315661.

PV of leasing

Here no tax rate is given, So it is ignored. So PV of Tax Shield on Lease payment also ignored.

PV of Lease payment = Annual lease payment X PV Factor for corresponding year.

PV factor = 1/(1+i)ⁿ, n = corresponding number of the years, i = 10% or 0.1,

year	PV Factor	Maintenance Cost PA	PV of Maintenance cost
1	0.909090909	$                     25,000.00	$                           22,727.27
2	0.826446281	$                     25,000.00	$                           20,661.16
3	0.819616417	$                     25,000.00	$                           20,490.41
4	0.812842997	$                     25,000.00	$                           20,321.07
5	0.806125552	$                     25,000.00	$                           20,153.14
6	0.799463622	$                     25,000.00	$                           19,986.59
7	0.792856747	$                     25,000.00	$                           19,821.42
8	0.786304472	$                     25,000.00	$                           19,657.61
9	0.779806345	$                     25,000.00	$                           19,495.16
10	0.773361921	$                     25,000.00	$                           19,334.05
		$                     25,000.00	$                       2,02,647.88
	PV of Lease payment will be		$                       3,54,914.26

PV of lease payment will Make more cash outflow, So Malaika will consider for buying the Machine.

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