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:

$F_{1} = \ 56,250\\F_{2} =\ 60,187.5\\F_{3} = \ 66,265.6\\F_{4} = \ 73,699.2$

Step-by-step 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

$F_{1} = \ 56,250\\F_{2} =\ 60,187.5\\F_{3} = \ 66,265.6\\F_{4} = \ 73,699.2$