Question

Assumptions and Calulated Values Bank Rate Information: Colin's Bank Account Rate (compounded monthly) Monthly Bank Rate Effective Annual Interest Rate 6.0000% 0.5000% 6.1678% Salary and Bonus Information: Annual Salary (4% COLA adjustment) Monthly Salary Discount factor (based on Cell B4 above) Discounted Annual Salary Year 1 $504,000 42,000 11.6189

Please provide the calculation for the discounted annual salary and explanation. Can you also explain how the discount factor was obtained. Have a great day.

Answer 1

interest rate	0.50%
month	Cash Flow	working : factor= 1/(1+r)^n (r= 8.00%)	present value factor = 1/(1+r)^n	after tax present value = Cash flow * discount value
1	42,000	1/ (1+0.08)^1	1.00	$   41,791.04
2	42,000	1/ (1+0.08)^2	0.99	$   41,583.13
3	42,000	1/ (1+0.08)^3	0.99	$   41,376.25
4	42,000	1/ (1+0.08)^4	0.98	$   41,170.40
5	42,000	1/ (1+0.08)^5	0.98	$   40,965.57
6	42,000	1/ (1+0.08)^6	0.97	$   40,761.76
7	42,000	1/ (1+0.08)^7	0.97	$   40,558.96
8	42,000	1/ (1+0.08)^8	0.96	$   40,357.18
9	42,000	1/ (1+0.08)^9	0.96	$   40,156.40
10	42,000	1/ (1+0.08)^10	0.95	$   39,956.61
11	42,000	1/ (1+0.08)^11	0.95	$   39,757.82
12	42,000	1/ (1+0.08)^12	0.94	$   39,560.02
	Total		11.6189	$ 487,995.15

The value of discounted factors can be understood by the above table, how it is calculated manually.

As we can see in the above table, the sum of the discounted factors for 12 months is 11.62.

And the annual discounted salary can also be calculated as , 42000*11.6189= $487,995.15

                       

Alternatively,

Also there is a formula for obtaining the Present Value of periodic payment= P* (1- (1+r)^-n)/r

So the discounted factor = (1- (1+r)^-n)/r

N=12

R=0.50%

DF= (1- (1+0.005)^-12)/0.005

= 11.6189.