Question

Maintenance money for a new building has been sought. Mr. Price would like to make a donation to cover all future expected maintenance costs for the new building. These maintenance costs are expected to be 50,000 for the first increasing by 2000 per year for the first 10 years, 70000 for the 11th year increasing by 3% per year for the following 20 years and 130000 each year after that. There is also an additional overhauling cost of 200000 for the building every 20 years. The donation will be placed in an account that will pay 12% interest.

A- Detetermine the amount of this donation

B. What is the equivalent annual maintenance cost over the infinite service life of the building

Answer 1

A- To detetermine the amount of this donation
We need to calculate in parts & add up the anwers of all parts as follows :
Part--1
PV at Year 0 ,of maintenance costs for the 1st 10 years=
Year	1	2	3	4	5	6	7	8	9	10
Annual maint.costs	50000	52000	54000	56000	58000	60000	62000	64000	66000	68000
PV F at 12%	0.89286	0.79719	0.71178	0.63552	0.56743	0.50663	0.45235	0.40388	0.36061	0.32197
PV at 12%	44642.86	41454.08	38436.13	35589.01	32910.76	30397.87	28045.65	25848.53	23800.26	21894.18
NPV	323019.33

Part--2

70000 for the 11th year increasing by 3% per year for the following 20 years

ie.

PV at Yr. 0

of the PV at end yr. 10 of the growing annuity starting with $ 70000 in year 11

growing at g=3% for years 12 to 20

ie. n=10

at an interest rate of 12% p.a.

using PV of Growing annuity formula,

PV(GA)=(P/(r-g))*(1-((1+g)/(1+r))^n)

ie.70000/(12%-3%)*(1-(1.03/1.12)^10)=

441229.36

PV at yr. 0 of the PV(GA) at end Yr. 10 =

441229.36/1.12^10=

142064.05

Part--3

130000 each year after that

ie. From yr. 21 onwards

so, we need to find

the PV at Yr.0

of the PV at   Yr. 20 end

of the perpetuity of $ 130000 per year

at r=12%

PV at Yr 20 end of the perpetuity =

130000/12%=

1083333.33

PV at Yr.0 of the above PV of perpetuity=

1083333.33/1.12^20=

112305.66

Part--4

additional overhauling cost of 200000 for the building every 20 years

PV at Yr. 0 of the perpetuity

of the PV of a single sum at end Yr. 20

PV of the single sum of $ 200000 at end of 20 years=

200000/1.12^20=

20733.35

PV at Yr. 0 of the above sum perpetually =

20733.35/12%=

172777.92

Answer for A =
Sum of all the PVs at yr 0
Part--1	323019.33
Part--2	142064.05
Part--3	112305.66
Part--4	172777.92
Amt. of this donation	750166.95

B. Equivalent annual maintenance cost over the infinite service life of the building

750166.95/20 yrs.=

37508.35