Exam 2 Formula Sheet
𝐹𝑉
𝑃𝑉 = (1 + 𝑟)𝑡
FV = PV(1 + r)t
𝐹𝑉
1
𝑡
𝐹𝑉
)
𝑃𝑉
𝑙𝑛(
𝑟 = (𝑃𝑉) – 1
𝐶
𝑡 = 𝑙𝑛(1 + 𝑟)
𝐶
𝐶
𝐶
𝑃𝑉𝑚𝑢𝑡𝑖𝑝𝑙𝑒 𝐶𝐹 = ∑𝑛𝑡=0 (1 +𝑡r)𝑡 = (1 +0r)0 + (1 +1r)1 + ⋯ + (1 +𝑛r)𝑛
𝐹𝑉𝑚𝑢𝑡𝑖𝑝𝑙𝑒 𝐶𝐹 = ∑𝑛𝑡=0 𝐶𝑡 (1 + r)𝑛−𝑡 = 𝐶0 (1 + r)𝑛−0 + 𝐶1 (1 + r)𝑛−1 + ⋯ + 𝐶𝑛 (1 + r)𝑛−𝑛
é
1 ù
ê1t ú
(1+
r)
ú
PVAnnuity = C ê
ê
ú
r
ê
ú
ë
û
é (1+ r)t -1ù
FVAnnuity = C ê
ú
r
ë
û
Annuity Due = (Ordinary Annuity Value) x (1 + r)
𝐶
PVperpetuity = 𝑟
Annual Percentage Rate = (rate per time period) x (number of time periods per year)
Rate per time period =
Annual Percentage Rate
.
Number of time periods per year
é
APR ù
EAR = ê1 +
ú - 1
m û
ë
m
1
é
ù
APR = m ê(1 + EAR) m - 1ú
ë
û
Simple interest per period = (principal) x (r)
Periodic interest = (periodic interest rate) x (beginning period balance)
Net Present Value (NPV) = PV of future cash flows – Investment cost
𝐶
C
C
C
C
1
2
3
𝑛
Net Present Value (NPV) = ∑𝑛𝑡=0 (1 +𝑡r)𝑡 = C0 + (1+r)
1 + (1+r)2 + (1+r)3 + (1+r)𝑛
Payback period = number of time periods that pass before the sum of the investment’s cash
flows equals the cost of the investment
𝐵
Payback Period = 𝐴 +
𝐶
A is the last full time period before you get back the cost of the investment
B is the value of the cost to recover at the end of time period A
C is the total cash flow during the period following time period A
Internal rate of return (IRR) = Discount rate or required return that makes the net present value
of an investment zero
IRR formula:
𝐶𝑡
C1
C2
C3
C𝑛
0 = ∑𝑛𝑡=0 (1 + IRR
=
C
+
+
+
+
0
𝑡
1
2
3
)
(1+IRR)
(1+IRR)
(1+IRR)
(1+IRR)𝑛
Crossover rate difference in Cash flows per period =
(cash flows from one project per period)
– (cash flows from second project per period)
Once we find these differential cash flows, we use them to find the IRR