Ranade Center for the Athletic Arts is a for-profit entity co-located with Ranad
ID: 2720051 • Letter: R
Question
Ranade Center for the Athletic Arts is a for-profit entity co-located with Ranade University.Their ATMARR is 12% and they pay taxes at 34%. The CEO of the Ranade Center is consideringbuilding a new tennis facility and has two choices:
Five and a half years later, you are doing a post-mortem analysis of the project anddiscover that while the Small Center had a salvage price of $2 million, the Bigger Center was, infact, sold for $5 million. How does this change your analysis, if at all?
Small Center Bigger Center Initial Cost $11 million $33 million Uniform Annual Benefit $3 million $9 million Estimated Salvage Value $2 million $3 million Depreciation Method SOYD SOYD Life 5 years 5 yearsExplanation / Answer
To answer the question, we should compare both methods, we have the datas required like the rate of return , salvage value, time, using these informations we would calculate the the Present Value of both the projects, the project in which the present value of benefit would be higher than the initial cost, that tennis court would be benefiacial financially.
Lets first define the depreciation methos:
SODY = Sum of years digits Depreciation. where dep for the yr is calculated as [(A-S)* (N-t+1)]/ First N integer.
For our example N = 5 yrs. so first 5 integer = N(N+1)/ 2= (5*6)/2= 15.
Lets compare the two projects.
Small Centre Big Centre.
Initial Cost (A) 11 million 33 million.
Salvage Value (S) 2 3 million.
Annual Benefit 3 million 9million.
No. oF years and Rate of return for both are 5 yrs and 15 %.
Depreciation calculated as per above formula: see below.
Net benefit each year= annual benefit - dep = X if this is positive then tax would be applicable = benefit- dep-tax.
Yr 1: 3- 3 mill = 0 9-10 = -1
Yr2: 3- 2.4 =.6 *(1-.34)= .39 9-8 =1*(1-.34)=.66
yr 3 3 -1.8 =1.2 (1-.34)=.7920 9-6= 3(1-.34)=1.98
yr 4 3-1.2 =1.8 (1-.34)= 1.188 9-4=5 (1-.34)=3.3
yr 5 3-.6=2.4 (1-.34)= 1.584+2= 3.584 9-2=7 (1-.34)=4.62+3=7.62
Putting this data we would calculate the PV of the project using rate of return of 15%. 3.27m(small cen) 6.60m(large
Thus , in both cases the PV is less than the initial cost, so no project should be undertaken.
This answer is prepared assuming the net benefit is taxable, and net benefit is used for calculation. If the benefit is not taxable, answer may differ.
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