This question introduces you to the concept of an annuity with growth. The formu

Question

This question introduces you to the concept of an annuity with growth. The formulae is given on p.3, equation (7), of the Note on Formulae, but I would encourage you to try doing it in Excel as well. (If the first cash flow is C, the next one will be C(1+g), and so on, where g is the growth rate in cash flow). As an example, the present value of an annuity that starts one year from now at $100, and grows at 5%, with the last cash flow in year 10, when the discount rate is 7%, is $860. Confirm this before attempting the problem using both the formula and excel. What is the NPV of of a new software project that costs $900,000 today, but has a cash flow of $180,000 in year 1 that grows at 7.0% per year till year 20? Similar investments earn 7.6% per year.

Explanation / Answer

Particulars Time PVF Amount PV Cash Outflows                                    -                  1.0000          (900,000.00)          (900,000.00) PV of Cash Outflows          (900,000.00) Cash Inflows                               1.00                0.9294            180,000.00            167,286.25 Cash Inflows                               2.00                0.8637            192,600.00            166,353.42 Cash Inflows                               3.00                0.8027            206,082.00            165,425.80 Cash Inflows                               4.00                0.7460            220,507.74            164,503.35 Cash Inflows                               5.00                0.6933            235,943.28            163,586.05 Cash Inflows                               6.00                0.6444            252,459.31            162,673.86 Cash Inflows                               7.00                0.5988            270,131.46            161,766.75 Cash Inflows                               8.00                0.5565            289,040.67            160,864.71 Cash Inflows                               9.00                0.5172            309,273.51            159,967.69 Cash Inflows                             10.00                0.4807            330,922.66            159,075.68 Cash Inflows                             11.00                0.4468            354,087.24            158,188.64 Cash Inflows                             12.00                0.4152            378,873.35            157,306.55 Cash Inflows                             13.00                0.3859            405,394.49            156,429.37 Cash Inflows                             14.00                0.3586            433,772.10            155,557.09 Cash Inflows                             15.00                0.3333            464,136.15            154,689.67 Cash Inflows                             16.00                0.3097            496,625.68            153,827.09 Cash Inflows                             17.00                0.2879            531,389.47            152,969.32 Cash Inflows                             18.00                0.2675            568,586.74            152,116.33 Cash Inflows                             19.00                0.2486            608,387.81            151,268.10 Cash Inflows                             20.00                0.2311            650,974.96            150,424.60 PV of Cash Inflows        3,174,280.33 NPV        2,274,280.33

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