Question

3. Is it really a good investment? Note: In these situations, PV and FV will be given, as well as the investment timeframe (NPER); use Excel’s =RATE formula to calculate the annual rate of return. Input PV as a negative number in order for Excel’s RATE function to operate correctly. The PBS TV program Antiques Roadshow features expert appraisals of art, furniture, pottery, and other such antiques. Often, people buy antiques speculatively, hoping their value will rise and they will turn out over time to be a good investment. Deploy your knowledge of asset valuation using Excel formulas to calculate the investment return in the following cases.

a. Marylouise Salas bought a Federal period chest from an antique store in 1975 for $800. In 2005, Leigh Keno appraised it at $8,000. Calculate Marylouise’s rate of return, assuming she sold the chest in 2005 for the appraisal value.

b. Bud Simonson bought an original 1931 Frankenstein movie poster at a garage sale in 1991 for $50. In 2015, Craig Flinner appraised the poster at $1,500. Calculate Bud’s rate of return, assuming he sold the poster in 2015 for the appraised value.

c. In case a) above, $800 in 1975 had the same inflation-adjusted buying power as $2,900 in 2015, according to the BLS Inflation Calculator: http://www.bls.gov/data/inflation_calculator.htm Recalculate Ms. Salas’ rate of return using the real (inflation-adjusted) initial value.

d. In case b) above, $50 in 1991 had the same inflation-adjusted buying power as $87 in 2015, according to the Inflation Calculator. Recalculate Mr. Simonson’s rate of return using the real (inflation-adjusted) initial value.

e. If our benchmark rate of return for long-term investments is the 7% real average broad stock-market return, who earned an economic profit from the antique investment? Did anyone earn an accounting loss? An economic loss?

Answer 1

a) Computation of Marylouise rate of return
Present value	-800	Value at which antique was bought
Future value	8000	Value at which antique was sold
Term	30	Holding period ie. 1975 to 2005
Rate	7.98%	(using Rate function "=rate(30,0,-800,8000)")
(ie.)Accounting Rate of return is 7.98% p.a.
b)Computation of Bud Simonson rate of return
Present value	-50	Value at which antique was bought
Future value	1500	Value at which antique was sold
Term	24	Holding period ie. 1991 to 2015
Rate	15.23%	(using Rate function "=rate(24,0,-50,1500)")
(ie.)Accounting Rate of return is 15.23% p.a.
c) Computation of Marylouise rate of return after adjusting for inflation
Present value adjusted for inflation	-2900	Value at which antique was bought after adjusting for inflation
Future value	8000	Value at which antique was sold
Term	30	Holding period ie. 1975 to 2005
Rate	3.44%	(using Rate function "=rate(30,0,-2900,8000)")
(ie.)Economic Rate of return is 3.44% p.a.
d)Computation of Bud Simonson rate of return after adjusting for inflation
Present value adjusted for inflation	-87	Value at which antique was bought after adjusting for inflation
Future value	1500	Value at which antique was sold
Term	24	Holding period ie. 1991 to 2015
Rate	12.60%	(using Rate function "=rate(24,0,-87,1500)")
(ie.)Economic Rate of return is 12.60% p.a.
e)Conclusion
(i) When comparing the above economic rates of return (c &d above) with the benchmark return of 7%, Bud Simonson
earned economic profit from the anitque investment (ie. Bud's Economic rate of return is more than 7%)
(ii) When comparing the above accounting rates of return (a &b above) with the benchmark return of 7%, none of
them incurred accounting loss from the anitque investment
(iii) When comparing the above economic rates of return (c &d above) with the benchmark return of 7%, Marylouise
incurred economic loss from the anitque investment (ie. Marylouise's Economic rate of return is less than 7%)