Question

Assume that Whee, Cheatham, and Howe is an auditing firm that has found that its summer interns are subject to a 50 percent learning curve for one of its important tasks, proofreading financial statements. For one of its interns, Kim Down, the firm has started to analyze the relation between time and financial statement proofreading Financial Statements Proofread (X) Time Required to Proofread the Xth Financial Statement 6.eeee hours 3. eeee hours Required: a. Compute the time required to proofread 4, 8, and 16 financial statements b. Assume that Kim's labor time costs $11 per hour. Compare the cost of proofreading the 1st financial statement to the cost of proofreading the 16th financial statement. What is the percentage of the cost of proofreading the 16th financial statement to the cost of proofreading the 1st financial statement?

Answer 1

Solution:

(a) The standard equation for the learning curve: T_n=T₁n^b

Here,

n is the number of financial proofread

T_n = Amount of time required to read n proofreads

T₁ = Amount of time required to read first financial proofread

b = learning curve factor which is equals to ln(p) / ln(2)

here ln(p) is the natural logarithm pf p

p =percentage of learning (in this case it is 50%)

Using the information given in the question:

b = ln(0.5) / ln(2) = -1

Number of financial proofreads	T1nb	The time required to read	hours * 60
1	6*(1-1)	6 hours	360 minutes
2	6*(2-1)	3 hours	180 minutes
4	6*(4-1)	1.5 hours	90 minutes
8	6*(8-1)	0.75 hours	45 minutes
16	6*(16-1)	0.375 hours	22.5 minutes

(b) The labor time cost is $11 per hour.

Cost of financial proofreading = Cost per hour * Number of hours required to read

Cost of proofreading 1st financial statement = $11 * 6 hours = $66

Cost of proofreading 16th financial statement = $11 * 0.375 hours = $4.125

The percentage of proofreading cost for 16th year to cost of proofreading for 1st year =

= Cost of proofreading 16th financial statement / Cost of proofreading 1st financial statement

= $4.125 / $66

= 0.0625 = 6.25%