Question

Average starting salaries for students using a placement service at a university have been steadily increasing. A study of the last four graduating classes indicates the following average salaries:

$60,000, $72,000, $84,500, and $96,000 (last graduating class).
(a) Predict the starting salary for the next graduating class using a simple exponential smoothing model with α = 0.25. Assume that the initial forecast was $55,000.

Answer 1

Given Information:

Smoothing constant = α = 0.25

Initial forecast salary = F₀ = $55,000

Actual salaries = A = $60,000, $72,000, $84,500, and $96,000

Required Information:

Forecast salaries = F = ?

Answer:

`F_(1) = \$56,250\\F_(2) =\$ 60,187.5\\F_(3) = \$66,265.6\\F_(4) = \$73,699.2\\`

Explanation:

The exponential smoothing model is given by

`F_(n) = \alpha \cdot A_(n - 1) + (1 - \alpha ) F_(n - 1)`

Where

`F_(n)` is the forecast salary for nth graduate class

α is the smoothing constant

`A_(n-1)` is the actual salary of n - 1 graduate class

`F_(n-1)` is the forecast salary of n - 1 graduate class

For n = 1

`F_(1) = 0.25 \cdot A_0} + (1-0.25) \cdot F_(0)\\F_(1) = 0.25 \cdot 60,000} + (0.75) \cdot 55,000\\F_(1) = 56,250`

For n = 2

`F_(2) = 0.25 \cdot A_1} + (1-0.25) \cdot F_(1)\\F_(2) = 0.25 \cdot 72,000} + (0.75) \cdot 56,250\\F_(2) = 60,187.5`

For n = 3

`F_(3) = 0.25 \cdot A_2} + (1-0.25) \cdot F_(2)\\F_(3) = 0.25 \cdot 84,500} + (0.75) \cdot 60,187.5\\F_(3) = 66,265.625`

For n = 4

`F_(4) = 0.25 \cdot A_3} + (1-0.25) \cdot F_(3)\\F_(4) = 0.25 \cdot 96,000} + (0.75) \cdot 66,265.625\\F_(4) = 73,699.218`

Therefore, the foretasted starting salaries are

`F_(1) = \$56,250\\F_(2) =\$ 60,187.5\\F_(3) = \$66,265.6\\F_(4) = \$73,699.2\\`