Question

Q) A company XYZ plans to purchase a production line that costs annually 50,000 AED paid at end of each year for ten years. Starting the end of second year, the annual payment increases by amount of 5,000 AED over the 10 years period. If the interest rate is 10% answer the following questions

1. What is the present worth of the annual amount?
2. What is the present worth of the gradient payments?
3. What is the total present worth of the payment?
4. What is the equivalent annual payment?

Q)The numerical value of the factor (P/A, 4%, 18) Is Hint: example of answer input e.g. 3.3333

Answer 1

Annual payment = 50,000 AED; gradient payment = 5,000 AED (increasing every year from 2nd year onwards); interest rate (r) = 10%; time period (n) = 10 years

Using this data, we have:

Time period (n)	Annual Payment (AP)	Gradient Payment (GP)	Total Payment P (AP+GP)	Present worth of AP (AP/(1+r)^n)	Present worth of GP (GP/(1+r)^n)	Present worth of the annual amount (P/(1+r)^n)
1	50,000	0	50,000	45,454.55	0.00	45,454.55
2	50,000	5,000	55,000	41,322.31	4,132.23	45,454.55
3	50,000	10,000	60,000	37,565.74	7,513.15	45,078.89
4	50,000	15,000	65,000	34,150.67	10,245.20	44,395.87
5	50,000	20,000	70,000	31,046.07	12,418.43	43,464.49
6	50,000	25,000	75,000	28,223.70	14,111.85	42,335.54
7	50,000	30,000	80,000	25,657.91	15,394.74	41,052.65
8	50,000	35,000	85,000	23,325.37	16,327.76	39,653.13
9	50,000	40,000	90,000	21,204.88	16,963.90	38,168.79
10	50,000	45,000	95,000	19,277.16	17,349.45	36,626.61
Total				307,228.36	114,456.71	421,685.07

a). Present worth of annual payment = 307,228.36 AED

b).  Present worth of gradient payment = 114,456.71 AED

c). Present worth of total payment = 421,685.07 AED

d). Equivalent annual payment can be calculated using the following formula:

NPV = present worth of total payment = 421,685.07 AED; r = 10% and n = 10

C = (10%*421,685.07)/(1-(1+10%)^-10)

= 421,68.51/0.61446

= 68,627.30 AED (Answer)