Assuming Positive Cash Flows and a Positive Interest Rate - Management Assignment Help

Assignment Task:

Task:

Answers to Critical Thinking and Concepts Review Questions

 

1.     The four elements are the present value (PV), the periodic cash flow (C), the discount rate (r), and the number of payments, or the life of the annuity, (t).

 

2.     Assuming positive cash flows and a positive interest rate, both the present and the future values will rise.

 

3.     Assuming positive cash flows and a positive interest rate, the present value will fall, and the future value will rise.

 

Answers to Basic questions

4.     To find the PVA, we use the equation:

 

        PVA = C({1 – [1/(1 + r)^t]} / r )

 

Computation of Present Value:
Particulars	Formula	Value
Annuity present value factor when r = 8%, t = 15	(1 – (1/(1+r)t))/r	8.5595
Present value when C = 6125	APVF*C	52 426.81
Particulars	Formula	Value
Annuity present value factor when r = 8%, t = 40	(1 – (1/(1+r)t))/r	11.9246
Present value when C = 6125	APVF*C	73 038.26
Particulars	Formula	Value
Annuity present value factor when r = 8%, t = 75	(1 – (1/(1+r)t))/r	12.4611
Present value when C = 6125	APVF*C	76 324.14
Particulars	Formula	Value
Present value when C = 6125, r = 8%, for perpetuity	C/r	76 562.50

      

 

Notice that as the length of the annuity payments increases, the present value of the annuity approaches the present value of the perpetuity. The present value of the 75-year annuity and the present value of the perpetuity imply that the value today of all perpetuity payments beyond 75 years is only $238.36

 

5.    Calculating Annuity Cash Flows:

Particulars	Formula	Value
Annuity present value factor when r = 11%, t = 6	(1 – (1/(1+r)t))/r	4.2305
Annuity value when present value is 15 000	PV/APVF	3545.65
Particulars	Formula	Value
Annuity present value factor when r = 7%, t = 8	(1 – (1/(1+r)t))/r	5.9713
Annuity value when present value is 21 400	PV/APVF	3583.81
Particulars	Formula	Value
Annuity present value factor when r = 8%, t = 15	(1 – (1/(1+r)t))/r	8.5595
Annuity value when present value is 145,300	PV/APVF	16 975.33
Particulars	Formula	Value
Annuity present value factor when r = 6%, t = 20	(1 – (1/(1+r)t))/r	11.4699
Annuity value when present value is 325,000	PV/APVF	28 334.98

 

6.     Computation of Present Value:

Particulars	Formula	Value
Annuity present value factor when r = 5%, t = 7	(1 – (1/(1+r)t))/r	5.7864
Present value when C = 1560	APVF*C	9026.74
Particulars	Formula	Value
Annuity present value factor when r = 10%, t = 9	(1 – (1/(1+r)t))/r	5.7590
Present value when C = 1280	APVF*C	7371.55
Particulars	Formula	Value
Annuity present value factor when r = 8%, t = 18	(1 – (1/(1+r)t))/r	9.3719
Present value when C = 20 000	APVF*C	18 7437.74
Particulars	Formula	Value
Annuity present value factor when r = 14%, t = 28	(1 – (1/(1+r)t))/r	6.9607
Present value when C = 53 200	APVF*C	370 307.23

 

7.    Computation of Annuity:

Particulars	Formula	Value
Annuity future value factor when r = 5%, t = 8	((1+r)t – 1)/r	9.5491
Annuity value when future value is 21 800	FV/AFVF	2282.94
Particulars	Formula	Value
Annuity future value factor when r = 7%, t = 40	((1+r)t – 1)/r	199.6351
Annuity value when future value is 1 500 000	FV/AFVF	7513.71
Particulars	Formula	Value
Annuity future value factor when r = 8%, t = 25	((1+r)t – 1)/r	73.1059
Annuity value when future value is 520 000	FV/AFVF	7112.97
Particulars	Formula	Value
Annuity future value factor when r = 4%, t = 13	((1+r)t – 1)/r	16.6268
Annuity value when future value is 98 700	FV/AFVF	5936.19

 

Answers to intermediate questions:

Intermediate

 

29.  The total interest paid by Simple Bank is the interest rate per period times the number of periods. In other words, the interest by Simple Bank paid over 10 years will be:

 

       0.063(10) = 0.63

 

       Complex Bank pays compound interest, so the interest paid by this bank will be the FV factor of $1, or:

 

       (1 + r)¹⁰

 

       Setting the two equal, we get:

 

       (0.063)(10) = (1 + r)¹⁰ – 1

       r = 1.63^1/10 – 1

       r = 0.0501, or 5%

 

30.  The timeline is:

 

 

0

1

…

60

$68 500

C

C

C

C

C

C

C

C

C

 

We need to use the PVA due equation, which is:

 

       PVA_due = (1 + r) PVA

 

       Using this equation:

 

Computation of Annuity:

 

Particulars	Formula	Value
Annuity present value factor when r = 0.375%, t = 60	(1 – (1/(1+r)t))/r	53.6394
Annuity value, when present value is 68 500	PV/APVF	1277.05
Annuity due	Annuity value*(1 + r)	1281.836

 

       r = 0.375 (4.5/12)

       $58 347.16 = $C{1 – [1 / (1 + 0.052 / 12)⁶⁰]} / (0.052 / 12)

       C = $1106.44

 

       Notice, to find the payment for the PVA due, we find the PV of an ordinary annuity, then compound this amount forward one period.

 

31.   The timeline is:

 

	0		1									…									12
	–$10 000																				FV

 

       Here we need to find the FV of a lump sum, with a changing interest rate. We must do this problem in two parts. After the first six months, the balance will be:

 

       FV = $10 000[1 + (0.009 / 12)]⁶

       FV =  $10 045.08

 

       This is the balance in six months. The FV in another six months will be:

 

       FV = $10 045.08 [1 + (0.185 / 12)]⁶

       FV = $11 010.72

        The problem asks for the interest accrued, so, to find the interest, we subtract the beginning balance from the principal. The interest accrued is:

 

        Interest = $11 010.72 – 10 000.00

        Interest = $1010.72

 

32.   We will calculate the time we must wait if we deposit in the bank that pays simple interest. The interest amount we will receive each year in this bank will be:

 

        Interest = $95 000(0.048)

        Interest = $4560 per year

 

        The deposit will have to increase by the difference between the amount we need and the amount we originally deposited, divided by the interest earned per year, so the number of years it will take in the bank that pays simple interest is:

 

        Years to wait = $255 000 – $95 000) / $4560

        Years to wait = 35.09 years

 

        To find the number of years it will take in the bank that pays compound interest, we can use the future value equation for a lump sum and solve for the periods. Doing so, we find:

 

	0		1								…									t
	–$95 000																			$255 000

 

       FV = PV(1 + r)^t

        $255 000 = $95 000 [1 + (0.048 / 12)]^t    

        t = 247 months, or 20.58 years

 

 

Challenge Questions:

 

58.  The timeline is:

 

	–24		–23		…	–12		–11		…	0		1				…	60
			$3583.33			$3583.33		$3833.33			$3833.33		$4083.33		$4083.33			$4083.33
											$200 000

 

 

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