Problem 6–6
1.
Present value of $1: n = ?, i = 8% (from Table 2, n = approximately 9 years)
2.
Annuity factor =
Present value of an ordinary annuity of $1: n = 5, i = ? (from Table 4, i =
approximately 7%)
3.
Annuity amount =
Present value of an ordinary annuity of $1: n = 10, i = 9% (from Table 4)
Problem 6–7
Requirement 1
Annuity amount =
Present value of an ordinary annuity of $1: n = 4, i = 10% (from Table 4)
Requirement 2
Annuity amount =
Present value of an ordinary annuity of $1: n = 5, i = 8% (from Table 4)
Requirement 3
Annuity factor =
Present value of an ordinary annuity of $1: n = ?, i = 10% (from Table 4, n = approximately
7 payments)
Requirement 4
Annuity factor =
Present value of an ordinary annuity of $1: n = 3, i = ?
Problem 6–8
Requirement 1
Present value of payments 4–6:
Present value of an ordinary annuity of $1: n = 3, i = 10% (from Table 4)
Present value $1: n = 3, i = 10% (from Table 2)
Present value of all payments:
Or alternatively:
Present value of an ordinary annuity of $1: n = 3, i = 10% (from Table 4)
From Table 4,
Requirement 2
Problem 6–9
Choose the alternative with the highest present value.
Alternative 1:
Alternative 2:
Present value of an annuity due of $1: n = 20, i = 7% (from Table 6)
Alternative 3:
Present value of an ordinary annuity of $1: n = 10, i = 7% (from Table 4)
Present value of $1: n = 9, i = 7% (from Table 2)
John should choose alternative 3.
Or, alternatively (for 3):
(difference due to rounding)
From Table 4,
or, From Table 6,
Problem 6–10
Present value of an ordinary annuity of $1: n = 5, i = 10% (from Table 4)
Present value of $1: n = 5, i = 10% (from Table 2)
Problem 6–11
Requirement 1
PVAD = Annuity amount x Annuity factor
Annuity amount =
Present value of an annuity due of $1: n = 10, i = 8% (from Table 6)
Requirement 2
Present value of an ordinary annuity of $1: n = 10, i = 8% (from Table 4)
Requirement 3
PVAD = (Annuity amount x Annuity factor) + PV of residual
Annuity amount =
Present value of $1: n = 10, i = 8% (from Table 2)
Present value of an annuity due of $1: n = 10, i = 8% (from Table 6)
Problem 6–12
Requirement 1
PVA = Annuity amount x Annuity factor
Annuity amount =
Present value of an ordinary annuity of $1: n = 10, i = 6% (from Table 4)
Requirement 2
Present value of an annuity due of $1: n = 20, i = 3% (from Table 6)
Requirement 3
Present value of an ordinary annuity of $1: n = 60, i = 1% (given)
Problem 6–13
Choose the option with the lowest present value of cash outflows, net of the
present value of any cash inflows. (Cash outflows are shown as negative amounts;
cash inflows as positive amounts)
1. Buy option:
Present value of an ordinary annuity of $1: n = 10, i = 12% (from Table 4)
Present value of $1: n = 10, i = 12% (from Table 2)
2. Lease option:
Present value of an annuity due of $1: n = 10, i = 12% (from Table 6)
Kiddy Toy should lease the machine.