Garland Inc. offers a new employee a single-sum signing bonus at the date of employment, June 1, 2018. Alternatively, the employee can receive $39,000 at the date of employment plus $10,000 each June 1 for five years, beginning in 2022. Assuming the employee's time value of money is 9% annually, what single amount at the employment date would make the options equally desirable?

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The single-sum equivalent would be $39,000 + the present value of a $10,000 deferred annuity. The present value of the deferred annuity on June 1, 2022, is an annuity due with n = 5 and i = 9%. That is, ($10,000 × 4.23972 from Table 6) = $42,397. To compute the equivalent of that amount at employment date, we take the present value of $42,397 where n = 4 and i = 9% from Table 2, which is $42,397 × 0.70843 = $30,035. Therefore, the single-sum equivalent would be $39,000 + $30,035 = $69,035.