BUSINESS FINANCE *Bolded Formula is not in Formula Sheet
BUSINESS FINANCE Week 1 Introduction Finance is study of how individuals, business and institutions acquire, spend, and manage financial resources. The main goal of managers is to maximise the market value of the firm, which maximise the wealth of shareholders. Managers however, do not always maximise the firm value. Reasons: - Managers may intend to maximise the value of the firm in the long-term in expense of the lower value in the short-term. - Agency Issues, where there is a conflict between the managers and the shareholders. 3
!"#$ &'()* = /41
,(.!/ ) 1+# /
E(CFt) = Expected Cash flow at time t n = Total number of periods r = Rate of return req. by Investors Simple Interest The value of cash flow is calculated without including any accrued interest to the principal. ∴ 67 = 89 1 + ; × = 67 ∴ 89 = (1 + ; × =) !3 − ?@ ∴3= ?@ × # !3 − ?@ ∴#= ?@ × 3 Compound Interest The value of cash flow is calculated with including any accrued interest to the principal. ∴ 67 = 89 1 + = 7 67 ∴ 89 = 1+= 7 !3 ∴#= ?@
1 3
∴ 3 = ABC (1D#)
−1 !3 ?@
Fn is the accumulated value at time n of amount of cash P0, with rate of return required by Investors r.
Perpetuities Perpetuities are series of equal, periodic cash flow that goes on forever. Suppose present are denoted by P0 and the equal periodic cash flow are denoted by C, E E E + +⋯+ 1+= 1+= F 1+= 7 1 1 1 89 = E 1 + + +⋯+ 1+= 1+= F 1+= 7 89 = E +
As 1 +
H HDI
+
H HDI J
+⋯+ 89 =
H HDI K
H
→ as ; → ∞ I
E =
Deferred Perpetuities Perpetuities that starts at some future dates Present value for perpetuities that started at period (n+1) is, E 89 = 1+= 7 = Ordinary Annuities ?@ NO , !3 (NO) Ordinary Annuities are series of equal, periodic cash flow paid at the end of each period, with last payment at time n. The accumulated value of these cash flows are denoted by 67 (QR) and the present value are denoted by 89 (QR). E E E + +⋯+ 1+= 1+= F 1+= 7 E E 1 + = ∙ 89 QR = E + +⋯+ 1+= 1 + = 7TH E 1 + = 89 QR − 89 QR = E − 1+= 7 1 = ∙ 89 QR = E ∙ 1 − 1+= 7 89 QR =
E 1 ∙ 1− = 1+= 7 E ∴ 67 QR = ∙ 1 + = 7 − 1 =
∴ 89 QR =
Deferred Ordinary Annuities ?@ UO , !3 (UO) Ordinary annuities that starts at some future date. 89 VR with payment starts at time t+1 is, . 1 ∴ ?@ UO = ∙ 1 + # / ∙ 1 − # 1+# 3 . ∴ !3 UO = ∙ 1 + # / ∙ [ 1 + # 3 − 1] #
*Bolded Formula is not in Formula Sheet
!"#$ &'()* = /41
,(.!/ ) 1+# /
E(CFt) = Expected Cash flow at time t n = Total number of periods r = Rate of return req. by Investors Simple Interest The value of cash flow is calculated without including any accrued interest to the principal. ∴ 67 = 89 1 + ; × = 67 ∴ 89 = (1 + ; × =) !3 − ?@ ∴3= ?@ × # !3 − ?@ ∴#= ?@ × 3 Compound Interest The value of cash flow is calculated with including any accrued interest to the principal. ∴ 67 = 89 1 + = 7 67 ∴ 89 = 1+= 7 !3 ∴#= ?@
1 3
∴ 3 = ABC (1D#)
−1 !3 ?@
Fn is the accumulated value at time n of amount of cash P0, with rate of return required by Investors r.
Perpetuities Perpetuities are series of equal, periodic cash flow that goes on forever. Suppose present are denoted by P0 and the equal periodic cash flow are denoted by C, E E E + +⋯+ 1+= 1+= F 1+= 7 1 1 1 89 = E 1 + + +⋯+ 1+= 1+= F 1+= 7 89 = E +
As 1 +
H HDI
+
H HDI J
+⋯+ 89 =
H HDI K
H
→ as ; → ∞ I
E =
Deferred Perpetuities Perpetuities that starts at some future dates Present value for perpetuities that started at period (n+1) is, E 89 = 1+= 7 = Ordinary Annuities ?@ NO , !3 (NO) Ordinary Annuities are series of equal, periodic cash flow paid at the end of each period, with last payment at time n. The accumulated value of these cash flows are denoted by 67 (QR) and the present value are denoted by 89 (QR). E E E + +⋯+ 1+= 1+= F 1+= 7 E E 1 + = ∙ 89 QR = E + +⋯+ 1+= 1 + = 7TH E 1 + = 89 QR − 89 QR = E − 1+= 7 1 = ∙ 89 QR = E ∙ 1 − 1+= 7 89 QR =
E 1 ∙ 1− = 1+= 7 E ∴ 67 QR = ∙ 1 + = 7 − 1 =
∴ 89 QR =
Deferred Ordinary Annuities ?@ UO , !3 (UO) Ordinary annuities that starts at some future date. 89 VR with payment starts at time t+1 is, . 1 ∴ ?@ UO = ∙ 1 + # / ∙ 1 − # 1+# 3 . ∴ !3 UO = ∙ 1 + # / ∙ [ 1 + # 3 − 1] #
*Bolded Formula is not in Formula Sheet
