**Unformatted text preview: **he painting, she realizes that its sale price in 5 years could
range between $30,000 and $140,000. Because of the high uncertainty surrounding the painting’s value, Celia believes that a 15% required return is
appropriate.
These two estimates of the appropriate required return illustrate how this
rate captures risk. The often subjective nature of such estimates is also clear. The Basic Valuation Model
Simply stated, the value of any asset is the present value of all future cash flows it
is expected to provide over the relevant time period. The time period can be any
length, even infinity. The value of an asset is therefore determined by discounting
the expected cash flows back to their present value, using the required return
commensurate with the asset’s risk as the appropriate discount rate. Utilizing the
present value techniques explained in Chapter 4, we can express the value of any
asset at time zero, V0, as
V0 CF1
(1 k)1 CF2
(1 k2) ... CFn
(1 k)n (6.5) 10. Although cash flows can occur at any time during a year, for computational convenience as well as custom, we
will assume they occur at the end of the year unless otherwise noted. CHAPTER 6 TABLE 6.5 283 Interest Rates and Bond Valuation Valuation of Groton Corporation’s Assets by Celia Sargent Asset Cash flow, CF Michaels Enterprises stockb Valuationa Appropriate required return $300/year indefinitely 12% V0 $300 (PVIFA12%,∞) $300
Oil wellc Year (t)
1
2
3
4 Original paintingd CFt 20% $ 2,000
4,000
0
10,000 15% $85,000 at end of year 5 V0 V0 1
0.12 $2,500 [$2,000 (PVIF20%,1)]
[$4,000 (PVIF20%,2)]
[$0 (PVIF20%,3)]
[$10,000 (PVIF20%,4)]
[$2,000 (0.833)]
[$4,000 (0.694)]
[$0 (0.579)]
[$10,000 (0.482)]
$1,666 $2,776
$0 $4,820
$9,262
$85,000 (PVIF15%,5) $85,000 (0.497) $42,245
aBased on PVIF interest factors from Table A–2. If calculated using a calculator, the values of the oil well and original painting would have been
$9,266.98 and $42,260.03, respectively.
bThis is a perpetuity (infinite-lived annuity), and therefore the present value interest factor...

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